202110722-PERFORM-STUDENT-WORKBOOK-MATHEMATICS-G09-FY_Optimized

PRACTICE SHEET - 3 (PS-3) 1. Sports academy planned to construct a 9. A heap of sand is in the shape of cone. The radius swimming pool of size 50 m × 25 m × 5 m and at the base of the heap is 14 m and the height of line its interior with tiles. What is the amount the heap is 6 m, find the volume of sand present. of soil that needs to be removed? If the cost of A tractor is brought to move the sand and it can removing 10 m3 of soil is Rs.300 and cost for 1 carry 20 m3 of sand in one trip. Determine the m2 of tiles work is Rs. 100, what is the total cost number of trips needed by the tractor to take of making the swimming pool. away the heap of sand. 2. A company wanted to purchase boxes to pack 10. A right triangle with sides 3 m, 4 m and 5 m was certain material The boxes of sizes 10 cm × 15 revolved about its 3 m side and 4 m side at two cm × 6 cm and 15 cm × 12 cm × 4 cm. If the cost different locations to make cones. Which cone of delivering the boxes is Rs. 10 per box, then had more volume? which box should be chosen to supply 2700 cm3 of material? How much will be savings in the cost 11. If the curved surface area of cone and a cylinder of delivery by selecting the low cost option? are equal determine the relation between their heights if the two solids have the same base 3. The outer size of a large warehouse was found radius. to be 20 m × 25 m × 10 m and to keep lower temperature inside the warehouse; insulation 12. A laddu making company makes a special was added to the walls and roof. No insulation chocolate laddu with two different layers. At was added on the floor. If the thickness of the the center is a ball of cashew nuts of diameter insulation is 0.5 m, then what is the capacity of 4 cm and surrounding it is a 1 cm thick layer of the warehouse? If the insulation was 1 m thick, chocolate. Determine the weight of the laddu if 1 find out the reduction in the capacity of the ware cm3 of cashew nuts weighs 1.5 gm and 1 cm3 of house. chocolate weighs 0.8 gm. (Use 4π = 4.2 ) 4. If the length of the box is doubled, its width 3 is tripled and its height is halved, what is the change in its volume? 13. Two spheres of diameter 6 cm and 8 cm are available in the market. A company wants to give 5. A milk tank collects the milk from various places them to school children after filling them with and then at the dairy it bottles the milk into 0.5 ice-cream. The cost of packing is more important litre bottles. If the tanker is 5 m in diameter and to the company than then the cost of ice cream. 7 m in length determine how many bottles are Which size of packing should the company filled at the dair? select? 6. A remote village is facing water problems. It has 14. If the side of a cube is a, the diameter and height two wells of sizes 7 m diameter, 10 m deep and of a cylinder and cone are also of size a and the 10 m diameter, 7 m deep. The soil around the diameter of the sphere and hemisphere is a, then well absorbs 1 m3 of water in a day for every 50 find the geometry which has the highest and m2 of contact with the soil (contact measured lowest ratio of volume to the total surface area. at the start the day) and due to evaporation 1 (Use 5 = 2.23 ) m3 of water will be lost for every 10m2 of water exposed to air. Determine which well should be 15. A meteor falls in a field and creates a crater of used by the panchayat for storing the water. 14 m diameter. When the owner visits the field, he finds the crater surface is covered with some 7. Ramu wants to fill a water can whose capacity shining particles. Determine the amount of soil is 31.4 litres. He keeps it below a tap whose displaced by the meteor and the area over which opening is 2 cm diameter and water flows out at the shining particles are present. a speed of 50 cm/s. How much time should Ramu wait for filling the can? (Use = 3.14) 16. 64 spheres of diameter d are melted to make one sphere. Determine the size of the final sphere. 8. Raju found a steel pipe of 10 cm outer radius and 3 cm inner radius with a length of 49 cm while 17. A quarter of a circle is revolved about one of the digging to plant a sapling. He sold the pipe at a radius lines, what will be the shape of the solid rate of Rs. 2 for every 100 grams of steel. If 1 cm3 formed? of steel weighs 8 grams then find the amount received by Raju after selling the pipe. 137

PRACTICE SHEET - 4 (PS-4) I. Choose the correct option. 1. The space occupied by a solid object is called its (A) Area (B) perimeter (C) total surface area (D) volume 2. During conversion of a solid from one shape to another, the volume of the new shape will be (A) Decrease (B) Increase (C) remain unaltered (same) (D) doubled 3. In a right circular cone, the cross section made by a plane parallel to the base is (A) a sphere (B) a hemisphere (C) a circle (D) a semi circle 4. The Shape of a gilli in the gilli-danda game is a combination of (A) A cone and a cylinder (B) Two cones and a cylinder (C) Two cylinders (D) Two cylinders and a cone 5. The volume of hollow sphere is ( )(4π R3 − r3 ) (A) ( )(4π R3 − r3 ) ( )(4π R3 + r3 ) ( )(4π R3 − r3 ) (D) 6 cm3 3 cm3 (B) (C) 2 cm3 3 cm3 6. The volume of a cone of diameter “d” and height “ h” is (A) π d2h (B) π d2h/12 (C) π d2h/4 (D) π d2h/5 7. If each of the dimensions of a rectangle is increased by 100%, then the area is increased by (A) 400% (B) 100% (C) 200% (D) 300% 8. The L.S.A of right circular cone of height 15cm and base diameter 16 cm is (A) 90 π (B) 110 π (C) 136 π (D) 200 π 9. Statement (A): The perimeter of semi circle is (π + 2) r units Statement (B): The perimeter of quadrant circle is (1/2)( π + 4) r units (A) Both A & B are False (B) Both A & B are True (C) A is true, B is false (D) A is false, B is true 10. Statement A: L.S.A of Right prism = (1/2)x( perimeter of base)x( height) Statement B: L.S.A of Right pyramid = (2/2)x( perimeter of base)x (Slant height) (A) Both A & B are False (B) Both A & B are True (C) A is true, B is false (D) A is false, B is true II. Short answer questions. 1. The dimensions of a room are 12m x 7m x 5m, then show that the diadonal of the room equals to 218 . 2. A bowl of thickness 2cm has an inner radius of 9 cm. apply the suitable formula and find the volume of metal required to make a bowl. 3. Compare the barrel shown in below figure and find which can hold more water? 138

PRACTICE SHEET - 4 (PS-4) III. Long answer questions. 1. A sphere of metallic sphere of radius 42cm is melted and recast into a number of cones, each of diameter 14cm and height 6cm. find the number of cones so formed. 2. A clock tower is in the shape of the figure given below. Examine the figure and find its surface area. ( 5 = 2.23) 139

Self-Evaluation Sheet Marks: 15 Time: 30 Mins 1. The total surface area of a box 1000 sq cm. The 5. A large cylindrical tank of size 10 m diameter length of two of its sides area 10 cm and 20 and 7 meter height has a tap at the bottom. If cm, Determine the third side of the box. Find the water flows out of the tap at a rate of 50 the volume of the box and the ratio of volume m3 per hour, then find the time after which the to the total surface area. (2 Marks) tank will be empty. (2 Marks) 2. The outer curved surface area of a cylinder 6. An ice cream seller has two brands of cone ice is 4 times the base area of the cylinder. If the creams. A cone whose diameter is 5 cm and height of the cylinder is 10 m, determine the height of 8 cm costs Rs. 50 and another cone diameter of the cylinder. Use π = 3.14 with a diameter of 6 cm and a slant length of 7 (2 Marks) cm costs Rs. 63. Which cone will have more ice cream for every rupee spent? (3 Marks) 3. In a municipal park, there were circular tables 7. A hot air balloon is flying with the balloon and above them there was a large umbrella diameter of 10 m. A bird hit the balloon and a which opened like a cone and provided shade. lot of air is lost from it. If the final diameter of The cloth needed to make one umbrella was the balloon was 6 m, find the amount of air lost. 22 m2 and the length of the cloth from the center to the edge was 3.5 m. Find the area for ( Use 43 π =4.2 ) (2 Marks) which the umbrella could provide shade. (2 Marks) 4. A balloon was losing air and its current diameter is 10 cm. Ravi takes it and then opens the knot and blows the air into the balloon to a size of 30 cm. find the ratio of the final area to the initial area of the balloon. Find the ratio of the final volume to the initial volume of air in the balloon. (Assume that the balloon is always spherical in shape) (2 Marks) 140

14. Statistics Learning Outcome By the end of this lesson, a student will be able to: • Determine the mean, median and mode of the • Convert the given data in grouped frequency given ungrouped data. distribution table. • Create graphical representations of the given data using Bar graphs, Histograms, and Frequency polygons. Concept Map Key Points secondary data. Counting the number of photos in the newspaper • Thefactsorfigureswhicharenumericalorotherwise collected with a definite purpose are called data. will be primary data. Getting the cricket score from Data is the plural form of the Latin word datum. the news paper will be secondary data. Statistics is the branch of mathematics which deals Census data released by the government will be with the extraction of meaningful information of secondary data. the data. Getting information of cricket score by watching in the stadium will be primary data but getting the Example: same while watching tv can be secondary data. Students’age,Student’sheight,Salaryofemployees • The data collected as it is by the investigator is called raw data. The difference between the largest of company, rainfall in a city, temperature inside a and smallest value in the data is called range of the room, runs scored by a batsman, etc. data. The number of times a quantity appears in • If the information was collected by the investigator the data is called its frequency. To determine the with a definite objective, then the data obtained number of times a data is obtained, for each value is called primary data. If the information gathered in the raw data a mark is made against a particular from a source which already had the information class interval and the total number of marks for a stored, the data obtained is called secondary data. given class interval (Tally marks) is the frequency Examples: for that class. The table in which the value and the A person checking pens in the shop to know its count of its occurrence (frequency) is available is price will be primary data. If the person asks the called frequency distribution table or ungrouped shopkeeper about the price of pens will be the 141

14. Statistics frequency distribution table. classes and subtract from the lower limit of the Example: A batsman has scored runs as given class intervals. below. The new frequency distribution table which is 0, 1, 4, 6, 0, 0, 2, 3, 4, 0, 6, 4, 4, 4, 0, 1, 1. converted into to continuous class intervals is This is raw data. Each of the data is allotted to a particular class Runs Tally Marks Frequency (-0.5) – 2.5 |||| ||| 8 interval and the total number of values allotted 2.5 – 5.5 |||| | 6 (Tally Marks) will be the frequency. 5.5 – 8.5 || 2 The frequency of 0 is 5, frequency of 1 is 3, frequency of 2 is 1, frequency of 3 is 1, frequency of 4 is 5 and The lower limit (-0.5) is not possible but has to frequency of 6 is 2. The frequency distribution table considered for calculations purposes. of the given data is as follows: Case ii: Continuous Class intervals Runs Tally Marks Frequency The data can also be represented in a continuous 0 |||| 5 class interval directly as 1 ||| 3 2 | 1 Runs Tally Marks Frequency 3 | 1 4 |||| 5 0 – 2 |||| ||| 8 6 || 2 2 – 4 || 2 4 – 6 |||| 5 6 – 8 || 2 • When a large amount of data is collected, the data Here the class interval 0 - 2 contains the values 0, 1, is grouped into classes or class intervals and their 2 - 4 contains the values 2, 3, class interval 4 - 6 size is called the class size or class width. In a given contains values 4, 5 and the interval 6 - 8 contains class, the least number is called the lower limit the values 6, 7. and the greatest number is called the upper class limit or upper limit. The frequency distribution • Bar graph is a pictorial representation of data representation in class interval form is called in which bars (rectangles) of uniform width are grouped frequency distribution. drawn with equal spacing between them on one axis (x-axis) depicting the variable and the values In a class interval a - b, the interval will include all of the variable are shown on the other axis (y-axis). the values starting from a and includes the value a The heights of the bars depend on the values of the and upto the value b and doesnot include the value variable. b. A gap is left between two consecutive bars because The class intervals are to be continuous without any the data is continuous in nature. break. In case of discontinuity, half the difference in the discontinuity of the class intervals is calculated Example: No. of sixers hit by our batsman Dhawan, and this difference is subtracted from all lower Dhoni, Kohli, Pandya in a particular match are limits and added to the upper limits. 1,4,6,3 respectively. This data can be represented as Example: A batsman has scored runs in this order 0, 1, 4, 6, 0, 0, 2, 3, 4, 0, 6, 4, 4, 4, 0, 1, 1. Case 1: Discontinuous Class intervals Runs Tally Marks Frequency 0–2 |||| ||| 8 3–5 |||| | 6 6–8 || 2 In the table, the class interval 0 - 2 contains the If the values to be plotted on x and y axis are large, values 0,1, the class interval 3 - 5 contains the then a suitable scale of the values is taken. values 3,4 and class interval 6 - 8 contains the values 6, 7. In this selection of class intervals, the Example: If the values on y-axis are Rs. 1000, value 2 is not included because the class intervals Rs. 2000, Rs. 2500, Rs. 3000, etc, then the values are not continuous. are scaled as 1 unit on y-axis is Rs. 1000 and the corresponding height of the bars will be 1, 2, 2.5, 3 One method to make the intervals is to take half units. 142 of the gap i.e., , and add it to the upper limits of the

14. Statistics • Histogram is a representation of data like bar Marks No. of Width of Length of graph, but it is used for continuous class intervals. scored students class rectangle Here the bars of equal width are plotted with the 0-10 10 height of bars representing the frequency of the 1 1 ×10 =1 particular class interval. There are no gaps between 10-20 10 consecutive rectangles. 2 In case the values on the axis are skipped, then 10 = 12=00000 0.2 such a situation is represented using a kink or a break on the axis. 20-30 5 10 = 12=05000 0.25 In a histogram, the areas of rectangles are proportional to the corresponding frequencies. 30-50 8 20 8 ×10 =4 The widths of rectangles are proportional to the 20 class interval and the length according to the frequencies. The histogram for the data will be as shown Example: The marks scored in a unit test are as follows: Marks scored No. of students 0-10 1 10-20 2 20-30 5 30-40 2 40-50 6 All the classes have equal size of 10 and thus the histogram of the data will be as shown: • Frequency polygons are used when the data is continuous and very large. It is useful for comparing two different sets of data of the same nature. Frequency polygon is obtained by joining the points which represent the class mark and frequency. Class mark = Upper limit + Lower limit 2 If the class size is not same for all the class, then If no class exists preceding the lowest class and no the height of the histogram in the large sized class class exists succeeding the highest class, addition should be changed proportionally. of two class intervals with zero frequency enables to make the area of the frequency polygon the Example: Marks scored in unit test are as follows same as the area of the histogram. Marks scored No. of students If the lowest class is 0, then the start point of the frequency polygon will on the negative side of the 0-10 1 axis. 10-20 2 Example: 20-30 5 The marks scored in a unit test are as follows: 30-50 8 Marks scored No. of students The last class interval 30 - 50 has a class size of 20 0-10 1 while the size of all other classes is 10. The 10-20 2 frequency to be represented for the class 30 - 50 20-30 5 will be 8 ×10 =4 30-40 2 20 40-50 6 There is no class preceding 0 - 10. The imaginary class interval preceding 0 - 10 will be (-10) - 0 and 143

14. Statistics the class mark of this class will be −10 + 0 = −5 . ∑∑x = in=1fi xi 2 ni =1fi The class preceding the highest class will be 50 - 60 50 + 60 and the class mark of this class will be 2 = 55 Example: The marks of students are recorded in form of frequency distribution table as shown Marks scored No. of students Class mark below: Imaginary class 0 −10 + 0 −5 Marks 10 20 30 40 50 (-10) - 0 2 = No. of students 3 2 1 3 2 0-10 1 0 + 10 = 5 The product of frequency ( fi ) and marks obtained 2 ( xi ) are calculated using the table as shown: 10-20 2 10 + 20 = 15 Marks (xi) No. of students fi xi 2 10 Frequency (fi) 30 3 20 30 20 2 40 20-30 5 + = 25 30 1 30 2 40 3 120 30-40 2 30 + 40 35 50 2 100 2 = = 120 − 25 = 95 n 40-50 6 40 + 50 = 45 ∑fi xi = 320 2 i=1 Imaginary class 0 50 + 60 = 55 ∑∑ Mean=, x ni=in1=f1=ifxi i 31=210 29.09 50-60 2 The frequency polygon for the given data is as • Median is that value of the given number of follows: observations, which divides it into exactly two parts. The data is to be arranged in ascending (or descending) order, the median of the ungrouped data is calculated as follows: o If the total number of observations (n) is odd, then the median is the value of  n +1 th observation.  2  o If the total number of observations (n) is even, then the median is the mean of the  n th and  n + 1 th observations.  2   2   Example: A set of data is given by the following numbers: 5, 8, 6, 1, 4, 3. • The mean or average of a number of observations Arranging the numbers in ascending order we get: is the sum of the values of all the observations 1, 3, 4, 5, 6, 8 divided by the total number of observations. It is There are 6 observations, n = 6 and is even number. denoted by the symbol . n =3 and  n + 1  = 3+1 = 4 Example: A set of data is given by the following 2  2  numbers: 5, 8, 6, 1, 4, 3. Let a be the  n th observation, a =4 =Mean,   x 5=+ 8 + 6 6+1 + 4 + 3 4.5  2  If grouped data is available, where is the Let b be the  n + 4 th observation, b =5 frequency of the observation , then the mean of  2  the data is given by, 144

14. Statistics Medi=an a=+2 b 4=+2 5 4.5 • Mode is that value of the observation which occurs most frequently, i.e., the observation with the maximum frequency is called mode. A given data set can have more than one value for mode. Example: i) 2, 5, 6, 6, 5, 3 This data has 5, 6 occurring maximum number of times (2 times). Mode of the data is 5, 6 ii) 3, 6, 9, 11, 2, 9, 9, 14 This data has 9 occurring maximum number of times (3 times) Mode of the data is 9. Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Pre-requisites • Frequency distribution Table PS – 1 • Mean, Median and Mode Statistics • Bar graphs, Histograms PS – 2 Worksheet for “Statistics” • Collection of Data PS – 3 Evaluation with Self Check • Presentation of Data PS – 4 or Peer Check* • Graphical Representation of Data - Bar PS – 5 Self Evaluation Sheet graphs, Histograms, Frequency polygons • Measures of Central Tendency – Mean, Median and Mode ---- 145

PRACTICE SHEET - 1 (PS-1) 1. Determine the largest and smallest values of the data and range of the data. i) 3, 25, 6, 22, 99, -5, 2, 23 ii) 1, 100, 0.5, 0.001, 5, 50 iii) A, I , T, K, Y, J, M, G, B, I 2. The pocket money of 20 students of a class is noted as follows. 36 40 38 33 28 35 30 29 32 34 32 25 21 33 39 31 25 34 24 39 Construct the frequency distribution table with a class size of 4 starting from 20 and a class size of 5 starting from 18. Indicate the values that are taken in each class 3. A student collects the date of birth (Day and Month) of 40 students in sheet of paper as shown below. Produce the frequency distribution table for the given data. Draw bar graph of the data. Also mention the month in which maximum number of students were born, the month in which least number of students were born. 14/2 21/3 21/6 5/9 29/8 9/2 5/1 2/8 2/2 5/1 12/5 16/8 26/5 15/1 19/8 19/4 2/6 12/1 22/2 3/10 4/11 21/3 25/8 5/11 24/3 27/7 27/1 18/7 3/8 24/11 3/3 21/3 24/7 18/6 16/3 9/11 29/12 23/1 25/10 21/8 1/2 9/10 19/1 24/2 13/7 1/2 15/3 13/12 7/3 14/6 4. The weights (kg) of 13 students is as follows: 40, 35, 29, 33, 36, 33, 36, 38, 33, 37, 26, 33, 39. i) What is frequency? Determine the frequency distribution table of the given data. ii) What is range? Determine the range of the data. iii) What is mean? What is the average weight of the students? iv) What is mode? Determine the mode of the data? v) What is median? Determine the median of the data? 146

PRACTICE SHEET - 2 (PS-2) 1. Give two examples of primary data and secondary data. 2. Can primary data be created using a newspaper? Give examples. 3. A student participating for a 100m running competition has recorded his running time (minutes) as follows. 12.87 10.8 12.99 10.51 10.94 11.68 11.96 10.14 10.43 11.96 10.13 10.35 11.77 11.6 11.24 11.95 12.26 11.71 10.54 11.75 11.02 10.84 10.05 10.91 Construct a grouped frequency distribution table and determine the number of times the student completed the 100 m distance in less than 11 minutes. 4. LED bulb manufacturer tested 100 bulbs to determine the life (in months) of the bulb. Construct grouped frequency distribution table with one class interval as 12-16 Determine the maximum and minimum life of the bulbs. Find the number of bulbs that lasted for 16 months or more. 5. A dice was thrown repeatedly 50 times and its number is recorded as follows 4623211334 6214424614 4445514435 1121655322 5341123323 Construct a frequency distribution table and determine the number which appeared the maximum number of times and the number which appeared minimum number of times. 6. An AC unit in a hospital is not functioning and is creating problem. The temperature was set to 18 °C and the room temperature was recorded from morning to evening every 15 minutes for 8 hours. The temperature readings (°C) were as follows. 17.8 18.3 17.7 18.7 19.4 19 19.9 19.3 19.3 17.9 17.6 17.8 18.9 18.2 18.3 17.5 18.8 17.1 18.2 17.4 19.7 17.2 17.4 18 18.3 19.7 17.8 19.8 18.7 17.7 17.4 17.9 Construct a grouped frequency distribution table and determine the temperature range which is most frequent if one of the class intervals is 18.5 - 19. 147

PRACTICE SHEET - 3 (PS-3) 80-90 20 1. The number of visitors to a particular museum 90-100 45 for the first six months of a year are given in the table below. Construct a bar graph and find out 100-110 15 the busiest month at the museum. 5. The population of 80 districts of our country is Month No. of visitors recorded and is as per the table. January 10,000 Population 0 - 2 2 - 3 3 - 4 4 - 5 5 - 7 7 - 8 (in lakh) February 14,000 No. of 16 10 14 10 18 12 districts March 8,000 April 22,000 Draw the histogram to represent the given data 6. The screen of mobile phones is found broken May 16,000 and the data regarding the breakage of mobile June 20,000 screens is surveyed in a particular company of 2. A movie reviewer has collected the information 200 people.The data regarding the period in regarding the total tickets sold for 7 famous which the screen was broken is collected and movies. Draw the bar graph for the data and tabulated as follows: mention movie for which the least number of tickets were sold. Time period when phone screen No. of phones cracked (month) Number of tickets sold Movie (in lakh) 0-4 10 Avatar 96 4-8 20 Simba 84 8-12 60 Minions 108 12-18 30 Babubali 2 144 18-24 80 URI 72 Represent the data as a histogram and find out how many mobile phone screens cracked in the Dangal 120 first 4 months. Sultan 48 7. A company wanted to know about employees who have worked with them for the maximum 3. The fire safety department has tabulated the period. The data regarding the years of work height of the buildings in order to decide upon done by the employees is as per the table. the kind of equipment needed by them. The data is as follows. No. of 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 years of No. of Floors in the 1 2 3 4 5 6 7 8 9 service building No. of buildings 50 45 60 10 30 20 5 5 5 No. of 50 25 30 15 10 40 15 5 employ- Provide the graphical representation of the given ees data. Construct a frequency polygon for the data 4. The marks obtained by students in a Maths test is given. as follows. Represent the data using a histogram 8. A company makes a survey to find out the age and determine the number of students who have of the employees and the number of employees scored 70 or more. whose annual salary is more than Rs. 5 lakh. The Marks No. of students data is as provided in the table. 0-10 10 Employee 24-30 30-36 36-42 42-48 48-54 54-60 age (years) 10-20 20 20-30 30 No. of 20 15 35 5 40 50 30-40 40 employees 40-50 35 Construct the frequency polygon for the given data. 50-60 25 60-70 50 70-80 30 148

PRACTICE SHEET - 3 (PS-3) 9. Government wanted to know the age of people living in two districts after implementing some health schemes. The number of people in a age group for the two districts is given the table. Age 1-9 11-19 21-29 31-39 41-49 51-59 61-69 71-79 81-89 group (years) No. of 100 150 180 260 350 200 160 60 40 people in Village A No. of 40 120 200 140 360 290 250 80 20 people in Village B 10. ADrsauwrvtehye frequency polygon for the data. of done to know the monthly income farmers based on the amount of land they own and the type of crop they make is as follows: Land owned by Income from rice Income from wheat farmers (acre) (Rs.) (in 000’s) (Rs.) (in 000’s) 0-0.5 2 4 0.5-1.0 4 7 1.0-1.5 5 9 1.5-2.0 8 10 2.5-3.0 11 14 3.0-3.5 15 16 3.5-4.0 16 17 Represent the data using frequency polygons. 149

PRACTICE SHEET - 4 (PS-4) 1. The runs scored by Kohli in 20 ODI matches in a 7. The daily earnings (in Rs.) of 10 different year are as follows: labourers are as follows: 91 1 77 89 72 23 44 79 61 19 98 19 8 1 17 15 15 44 63 79 341 337 171 273 190 348 289 163 211 203 Determine their median daily earnings. Determine the average number of runs scored by Kohli in the given year. 8. In a math class, the result of the 10 mark test was as follows. 2. The profits in lakhs made by a certain company 7 3 4 3 4 6 10 6 2 4 10 in a particular year are given below. Determine the median score and mode. -5 11 -4 1 6 -10 1 2 -6 5 4 3 9. A set of observations are as follows. Determine the mode of the given data. Determine the average monthly profit made by the company. (A positive number is profit and i) 7 11 7 12 20 9 5 14 8 12 7 8 14 18 negative number means loss to the company.) ii) 49 25 49 38 39 39 37 27 44 39 17 9 39 38 iii) 16 22 24 23 25 26 26 16 14 10 20 19 13 11 3. The number of visitors to a particular museum for the first six months of a year are given in the table below. Determine the average number of visitors to the museum. Month No. of visitors January 10,000 February 14,000 March 8,000 April 22,000 May 16,000 June 20,000 4. The weekly temperature readings were taken in a particular city and tabulated as follows: Temperature (°C) 30 32 34 36 38 40 42 44 No. of weeks 10 6 12 4 5 5 3 7 Determine the mean temperature of the city. 5. Rahul had a mango tree in his house and one summer he began to weigh the mangoes and put them according to their weights. At the end, the data of the weights of the mangoes and their quantity is as shown in the table. Determine the average weight of the mango that grew in the tree. Weight (gm) 80 87 90 93 98 105 160 190 260 No. of mangoes 5 6 10 2 3 4 10 25 10 6. The age of members of two families are given in the table. Determine in which family the median age is higher. Family A 26 62 60 37 27 17 56 67 70 10 39 Family B 66 15 87 54 83 3 76 48 90 18 6 45 150

PRACTICE SHEET - 5 (PS-5) I. Choose the correct option. 1. If a data has two modes, then it is called (A) unimode (B) Bimodel (C) No mode (D) all 2. Among the following a measure of central tendency (A) Mode (B) Mean (C) Median (D) All 3. The class mark of a class interval is (A) Upper limit – lower limit (B) 1/2*(Upper limit + lower limit) (C) Upper limit + lower limit (D) 1/2*(Upper limit - lower limit) 4. The Ogive (curved Graph) can be used to find (A) Mode (B) Mean (C) Median (D) All 5. The mean of the square of the numbers 0,1,2,……..,n is n (2n +1) (A) n(n+1) (B) (n +1) (C) (n +1)(2n +1) (D) 6 2 6 6. The algebraic sum of all the deviations of all the observations from their mean is (A) Zero (B) Negative (C) Positive (D) cant say 7. If the mean of x, 1 is a, then the mean of x3, 1 is x x3 (A) a(a2-3) (B) a(4a2-3) (C) a(3a2+4) (D) a(a2+4) 8. If the mean of a1,a2,a3, ………an is ā, then the mean of (2a1+3),(2a2+3) …(…D)…2ā.(+2a3n+3) is (A) ā (B) 2ā (C) 2ā - 3 9. Statement (A): In a data the most often repeated value is called mode Statement (B): The most common and widely used measure of central tendency is mean (A) Both A & B are False (B) Both A & B are True (C) A is true, B is false (D) A is false, B is true 10. Statement A: The branch of mathematics which deals with collection, classification and interpretation of data is called statistics Statement B: the father of statistics is Cantor (A) Both A & B are False (B) Both A & B are True (C) A is true, B is false (D) A is false, B is true II. Short answer questions. 1. The mean height of three students is 140 cm. one of the students Ranga height is 120 cm. The other two students, Raju and Ramu have the same height. Show That Ramu height is 150 cm. 2. Identify the scale used on the axis of following graph. Write the frequency distribution from it. 3. Read the following table and List out class interval and frequency. Marks <36 <38 <40 <42 <44 <46 <48 <50 No of students 0 3 5 9 14 28 32 35 151

PRACTICE SHEET - 5 (PS-5) III. Long answer questions. 1. The mean weight of 48 students in a class is 60kg. The mean weight of boys in the class is 70 kg. And that of girls is 46kg. Find the number of boys and the number of girls. 2. The grades of 36 students of a class are recorded as follows. A+ A A A A+ B C B C DBBCBAABB C C D D A+ A B C B A A A+ A+ B B C D C List the data in the form of a frequency distribution table. Which is the most common grade? 152

Self-Evaluation Sheet Marks: 15 Time: 30 Mins 1) A hotel owner recorded the bill amount (in Rs.) of 45 customers which are as follows: 66 48 44 92 41 78 47 99 50 82 89 67 63 51 55 43 58 80 40 94 89 78 95 46 80 64 69 67 76 97 74 55 47 98 43 58 50 62 72 65 86 87 70 100 41 Construct a grouped frequency distribution table and determine the number of customers who make a bill of Rs. 80 or higher. (2 Marks) 3) The weight of the students of a class is measured and tabulated as follows: Weight 15-18 18-24 24-27 27-30 30-33 33-39 39-42 (kg) No. of 1 10 6 2 8 12 8 students Determine the number of students whose weight is more than 30 kg. (4 Marks) 2) The number of students failed in different subjects in class 10 in a district is as follows. Subject No. of students failed (in hundreds) English 5 Hindi 6 Maths 10 Science 3 Social 4 Represent the data using a bar graph (2 Marks) 153

Self-Evaluation Sheet Marks: 15 Time: 30 Mins 4) The number of centuries scored by a cricketer 5) Find the mean, median and mode of the given throughout his career is as per the table given. set of observations. Experience 0-5 5-10 10-15 15-20 20-25 25-30 i) 9 7 10 4 2 4 6 5 8 4 in the game ii) 47 5 50 44 9 37 44 44 37 15 22 40 37 (years) iii) 16 22 24 23 25 26 26 16 14 10 20 19 13 No. of 3 10 8 2 6 3 (4 Marks) centuries Draw the frequency polygon for the given data. (3 Marks) 154

15. Probability Learning Outcome By the end of this lesson, a student will be able to: • Determine the probability of an event in a given trail. Concept Map Key Points Number of outcomes thatmake an event • The words ‘probably’, ‘doubt’, ‘most probably’, Probability of an event = Total number of outcomes ‘chances’ etc are used when an element of uncertainty is present. of the experiment Example: • The possible events in certain experiments (trails) There is a chance of raining Probably Raju will not come to the party. Experiment Type Possible Outcomes • An experiment in which the result cannot be stated Coin tossing Heads, Tails exactly or where there is a possibility of different results is called a random experiment. Game of Dice 1, 2, 3, 4, 5, 6 Examples: Tossing of coins, expecting rain on a particular day, Telephone Directory Digits in the phone number, etc. etc The uncertainty of ‘probably’, etc can be measured numerically by means of probability in many cases. Weather Forecast It rains, it does not rain on a • Each outcome of an experiment or a collection of given day outcomes make an event. Example: • A trail is an action which results in one or several Getting heads or tails in a coin tossing experiment outcomes. There can be several outcomes in an is an event. event. An event for an experiment is the collection Getting a particular number when a dice is thrown of some outcomes of the experiment. is an event. Example: Getting an odd number or even number when a i) Tossing a coin is a trail dice is thrown is an event. Getting a tail is the event with the outcome tail. • If there are multiple outcomes and each outcome ii) Throwing dice is a trail has an equal chance of occurring, then they are Get an even number is an event and the called as equally likely outcomes. outcomes could be 2, 4, 6. Example: • The experimental or empirical probability, P(E) of Getting heads or tails are equally likely events. an event E happening is given by: Getting any number when a dice is thrown are all No. of trails in which the event happened equally likely events. P(E)= Total no. of trails Getting an odd number and any other number are not equally likely events. Experimental or empirical probability is called as • If the outcomes of all events are equal, then probability. • The empirical probability depends on the number of trails undertaken and the number of times the desired outcome is obtained in the trails. • The probability of each event lies between 0 and 1. • The sum of all probabilities is 1. • The sum of probability of an event happening and the probability of an event not happening is always 1. 155

15. Probability Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Pre-requisites • Concept of Probability PS – 1 • Probability of events in simple experiments PS – 2 Quadratic Equation • Probability – An Experimental Approach PS – 3 Self Evaluation Worksheet for “Probability” Sheet Evaluation with Self Check ---- or Peer Check* 156

PRACTICE SHEET - 1 (PS-1) 1. Mentions the possible outcomes in the following experiments: i) A coin is tossed ii) A dice is thrown iii) A card is drawn from a pack of cards iv) In a basket ball game, the ball is thrown towards the basket. 2. In a bag of 20 plastic balls with numbers 1 to 20, determine the probability of the following events: i) Probability that the number on the ball is an odd number. ii) Probability that the number on the ball is 10. iii) Probability that the number on the ball is less than 8. iv) Probability that the number on the ball is greater than or equal to 16. 157

PRACTICE SHEET - 2 (PS-2) 1. An old man goes to the park for a walk every day vi) Team scores 5 goals and loses the match of the year and he met a young guy 60 times in vii)Inamatch,iftheteamhasscored2goalswhatis that year. Determine the probability for the fol- lowing events: the probability that it will win the match. 7. A dice is thrown 100 times and the following is i) The old man meets the young guy on a given day. the result: Number on the dice 1 2 3 4 5 6 ii) Theoldmandoesnotmeettheyoungguyagiven No. of appearance 30 20 22 15 3 10 day. Compute the probability of the following events: 2. On 50 occasions Raju sees an offer for a particular i) Getting each number when the dice is thrown. brand of shirts in a news paper and goes to ii) Getting an odd number when the dice is the shop. 40 times the offer was true and the remaining time the offer date was shifted due to thrown. some reason. Determine the probability for the iii) Getting an even number when the dice is following events. thrown. i) Raju goes to the shop after seeing the offer in the news paper. iv)Getting numbers greater or equal to 5 when the dice is thrown. ii) Raju does not get the offer when he goes to the shop. 8. Among the various movies made in India, some of them made a lot of money while a lot of them 3. The probability of the weather forecast being flopped at the box office. The table below gives true is 0.9 and Ravi verified the forecast 100 number of movies made and the money made by times. Determine the number of times the them. forecast was true and the number of time the forecast was false. Money made by Less 10 40 80 100 More movie (in crores) than to to to to than 4. Dravid and Laxman played 100 test matches together. In 20 batches both of them scored a 10 40 80 100 200 200 century and in 30 matches both of them scored a half century. Determine the probability of the No. of movies 100 80 60 52 5 3 following events. What is the probability that: i) Both batsmen scored more than 100 runs i) Movie will make a minimum of 100 crores ii) Both batsmen scored more than 50 runs ii) Movie will make 40 to 80 crores 5. Sita, Rita and Gita are three friends who always iii) Movie will make more than 200 crores iv) Movie will make less than 10 crores went together to hotel on weekends. In the past 9. A LED bulb manufacturer declared that the life one year the three friends went 60 times for dinner and 24 times they all had the same food, of a LED bulb was 2000 hours. A maintenance 17 times only two of them had ordered same engineer of another company purchased the food. Determine the probability for the following bulbs and recorded the amount of time a LED events: bulb worked fine before replacement. The data i) Three friends had the same food at the hotel. is as follows. ii) Three friends had different food at the hotel. 6. A football team’s one year scoring and their Bulb 0 - 500- 1000- 2000- 4000- More performance were tabulated as follows. worked 500 1000 2000 4000 6000 than fine (hour) 6000 No. of 50 60 90 250 300 250 bulbs No. of goals scored 12345 What is the probability that a bulb chosen at No. of matches played 30 20 25 15 10 random: No. of matches won 10 15 5 9 9 i) Worked for its stated life. ii) Did not work for its stated life. The team has either won the match or lost the iii) Failed after 2500 hours. match and there was never a tie (draw). What is 10. A village panchayat makes the survey about the the probability that: farmers in the village. The farmers produce only i) Team wins a football match one type of crop and do not change them. The ii) Team loses a football match data collected is as follows: iii) Team scores 4 goals in a match iv) Team scores 3 or less goals in a match v) Team scores 3 goals and wins the match 158

PRACTICE SHEET - 2 (PS-2) Crop of farmer Farmer’s income (in lakhs/year) Rice 0-1 1-2 2-3 3-4 4-5 Wheat 53102 Sugar Cane 34213 Vegetables 67214 13462 a) If a farmer is chosen at random, then what is the probability that: i) He grows a) Sugarcane crop b) Vegetables ii) He grows either rice or wheat? iii) Has an income of 3-4 lakh/year? iv) Has an income greater than 3 lakh/year b) What is the probability that a rice or wheat growing farmer makes more than 2 lakh/ year. 11. A survey conducted by a home appliances company to know the number of items their customers are having at home. The data from the survey is as follows: Age of customer No. appliances at home (year) 12345 25-35 36-49 60 65 40 15 10 50-60 20 40 50 30 20 10 50 80 50 30 What is the probability that i) A customer will have 3 or more items at his home. ii) A customer belonging to age group 36-49 and will have 5 appliances at his home. iii) A customer chosen at random will have a age more than 50 year and will have 2 or less items at his home. iv) A customer belongs to the age group 25-35. v) A customer will have age less than 36 and will have 4 or more items at his home. 159

PRACTICE SHEET - 3 (PS-3) I. Choose the correct option. 1. Among the following, which is not a face card? (A) King (B) Queen (C) Ace (D) Jack 2. The collection of all events is called (A) Equally likely events (B) Exhaustive events (C) Mutually exclusive events (D) can’t say 3. P(E) = 0.15 , then P(not E)= (A) 0. 65 (B) 0.75 (C) 0.85 (D) 0.15 4. The event \"Gandhiji’s birth day is on 2nd October\" is (A) Less likely (B) More likely (C) Certain (D) Impossible 5. Among the following, it cannot be the probability of an event is (A) 1 (B) 1 (C) 25% (D) 4 3 2 3 6. A Box contain 4 red cricket balls, 4 white cricket balls, 2 pink cricket balls, then the probability to get a pink cricket ball is (A) 2 (B) 1 (C) 1 (D) 1 5 5 10 2 7. The probability of baby born either boy (or) girl is (A) 1 (B) 1 (C) 0 (D) 2 2 3 8. The probability that a non leap year has 53 Sundays, is (A) 6 (B) 5 (C) 2 (D) 1 7 7 77 9. Statement (A): Each one of the events has an equal chance of occurrence is Equally likely events Statement (B): An event which will not occur on any account is called an impossible event (A) Both A & B are False (B) Both A & B are True (C) A is true, B is false (D) A is false, B is true 10. Statement A: P ( A) = Number of favourable outcomes for event A Number of total possible outcomes Statement B: The probability of an event is always lies between 1 and 2 (A) Both A & B are False (B) Both A & B are True (C) A is true, B is false (D) A is false, B is true 160

PRACTICE SHEET - 3 (PS-3) II. Short answer questions. 1. n an arithmetic progression, a = 2 , d = 2 and L = 14. Show that probability to select a number in above A.P is a multiple of three = 2/7. 2. A = {x/x is a prime number, x∈N , 0 < x < 20} . write roster form of set , get the probability of an even number by using probability formula. 3. The median of the data 1,2,3,4,7,x,14,15,17,20,25 is 10. Analyze the probability to get a number 10 from the above data. III. Long answer questions. 1. A piggy bank contains hundred 50 p coins, fifty ₹ 1 coins, thirty ₹ 2 coins and twenty ₹ 5 coins. The coins will fall out when the bank is turned upside down. Find the probability of the coin (i) will be a 50p coin. (ii) Will not be a ₹ 5 coin and (iii) will be either ₹ 1 coin or ₹ 2 coin. 2. If you drop a die at random on the rectangle region of length 4m and breadth 2m as shown in figure. Ana- lyze the figure and find probability that it will land inside the circle with radius 1m. 161

Self-Evaluation Sheet Marks: 15 Time: 30 Mins 1. Two events have a probability of 0.3 and 0.5. Which event is more likely to occur? (1 Mark) 3. In 100 test matches, the centuries made by the batman were analyzed and the data is as follow: Number of centuries 1 2 3 4 5 6 scored in a match Number of matches 12 15 34 20 10 5 In a randomly chosen match, what is the probability that: i) No centuries were scored. ii) At least 5 centuries were scored iii) A total of 2 or less number of centuries were scored iv) At least one century was scored (4 Marks) 2. In a month Rahul had tried to call Raju 120 times and Raju received the call only 25 times. What is the trial in this experiment and what are the possible outcomes? What is the probability that Raju receives Rahul’s calls? What is the probability that Raju does not receives Rahul’s calls?   (2 Marks) 162

Self-Evaluation Sheet Marks: 15 Time: 30 Mins 4. A soap company as part of the Deepavali sales 5. Government of India conducts a survey of 200 began to put randomly some gold coins in the towns regarding the population of towns and soap powder packets before final packing. In the hospitals available and the details are as one given day, it made 1,000 packets of soap follows: powder and has put 10 gold coins and one coin only in one packet. The company sent the soap No. of hospitals packet to five shops as per the table: Town population 1 2 3 4 5 0-15000 11 14 15 8 7 15000-30000 10 3 15 3 13 Shop A B CDE 30000-50000 9 3 7 11 13 No. of packet with 3 2 212 50000-1 lakh 8 14 12 9 15 gold coins No. of soap packets 200 300 100 50 350 What is the probability that: supplied i) a town with more than 50000 people has at If a person goes to buy soap powder, then what least 4 hospitals. is the probability that: ii) a town will have population less than i) A soap packet purchased in each of the five 15000. shops will have a gold coin in them. iii) a town will have exactly 2 hospitals iv) a town will have population of 15000-30000 ii) A packet picked from the lot of all manufactured soap powder packets of the and 3 or less hospitals. day will have a gold coin in it. (4 Marks) iii) A packet picked from the boxes to be supplied to shops C and D will have a gold coin. Determine the shop in which the soap powder be purchased so that there is the highest chance of getting the packet with gold coin. (4 Marks) 163

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