E-LESSON-2

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M.B.A 2 All right are reserved with CU-IDOL Quantitative Techniques for Managers Course Code: MBA602 Semester: First SLM Units: 2 E-LESSON : 2 www.cuidol.in Unit-2 (MBA602)

Introduction to Statistics 33 OBJECTIVES INTRODUCTION Student will be able to : The business environment of today being To describe the various quantitative techniques very complex and complicated, the decision available for understanding statistical data science. making for business is a very difficult job Learn the techniques of graphical representation of data. The statistical data constitutes the basic raw Learn about the Graphical Display of two-variable material, for its useful gain in decision continuous data using scatter plots. making. Learn about the frequency distribution and their In the previous chapter we elaborated as to applications in research. how the statistical data can be tabulated and presented in a form to draw a meaning inference at a glance www.cuidol.in Unit-2 (MBA602) INASllTITriUgThEt aOrFeDreISsTeArNveCdE AwNitDh OCNUL-IIDNOE LLEARNING

TOPICS TO BE COVERED 4 > Presentation and Analysis of Data > Frequency Distributions > Graphical Display of Data using Histograms, Frequency Polygons > Graphical Display of two-variable continuous data using scatter plots. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Charts and Graphs 5 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

FREQUENCY DISTRIBUTION 6 Frequency Distribution: A table that shows classes or Class Frequency intervals of data with a count of the number of entries in each class. It is used to organize data and helps to 1–5 5 recognize patterns. 6 – 10 8 11 – 15 6 The frequency, f, of a class is the number of data 16 – 20 8 entries in the class. 21 – 25 5 26 – 30 4 Each class has:  A lower class limit, which is the least number that can belong to the class (1, 6, 11, 16, 21, 26)  An upper class limit, which is the greatest number that can belong to the class (5, 10, 15, 20, 25, 30) www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

FREQUENCY DISTRIBUTION 7  The class width is the distance between lower (or Class Frequency upper) limits of consecutive classes. 1–5 5 6 – 10 8  Example: 6 – 1 = 5 11 – 15 6  The range is the difference between the maximum and 16 – 20 8 21 – 25 5 the minimum data entries. Example: if the maximum 26 – 30 4 data entry is 29 and the minimum data entry is 1, the range is 29 – 1 = 28 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Constructing A Frequency Distribution From A Data Set 1. Choose the number of classes (usually between 5 and 20) 8 2. Find the class width. a) Find the range of the data b) Divide the range by the number of classes c) Round up to the next convenient number 3. Find the class limits. a) Use the minimum data entry as the lower limit of the first class b) Find the remaining lower limits (add the class width to the lower limit of the preceding class). c) Find the upper limit of the first class. Remember that classes cannot overlap. d) Find the remaining upper class limits. 4. Tally the data 5. Count the tally marks to find the total frequency for each class www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Example: Constructing a Frequency Distribution 9  The following sample data set lists the number of minutes 50 Internet subscribers spent on the Internet during their most recent session.  Construct a frequency distribution that has seven classes. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 86 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44 www.cuidol.in Unit-2 (MBA602) All right are reserved8with CU-IDOL

Solution: Constructing a Frequency Distribution 10 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 86 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44 1. Number of classes = 7 (given) 2. Find the class width max min 86 7 11.29 #classes 7 Round up to 12 www.cuidol.in Unit-2 (MBA602) All right are reserved9with CU-IDOL

Solution: Constructing a Frequency Distribution 11  Find the class limits: Lower Upper  Use 7 (minimum value) as first lower limit. limit limit Add the class width of 12 to get the lower limit of the next class. Class width 7  7 + 12 = 19 = 12  Find the remaining lower limits. 19 31 43 55 67 79 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Solution: Constructing a Frequency Distribution 12  The upper limit of the first class is 18 (one Lower Upper Class less than the lower limit of the second limit limit width = 12 class). 7 18  Add the class width of 12 to get the upper limit 19 30 of the next class. 31 42  18 + 12 = 30 43 54 55 66  Find the remaining upper limits. 67 79 78 90 www.cuidol.in Unit-2 (MBA602) All right are reserv1ed1with CU-IDOL

Solution: Constructing a Frequency Distribution 13  Make a tally mark for each data entry in the row of the appropriate class.  Count the tally marks to find the total frequency f for each class. Class Tally Frequency, f IIII I www.cuidol.in 7 – 18 IIII IIII 6 19 – 30 IIII IIII 31 – 42 IIII III 10 43 – 54 IIII 55 – 66 IIII I III 13 67 – 78 II 79 – 90 8 5 6 2 Σf = 50 Unit-2 (MBA602) All right are reserved with CU-IDOL

Example: Constructing a Frequency Distribution 14  The following represents census data reporting the ages of the entire population of the 77 resdients of Akhiok, Alaska. Construct a frequency distribution with 6 classes. 28 6 17 48 63 47 27 21 3 7 12 39 50 54 33 45 15 24 1 7 36 53 46 27 5 10 32 50 52 11 42 22 3 17 34 56 25 2 30 10 33 1 49 13 16 8 31 21 6 9 2 11 32 25 0 55 23 41 29 4 51 1 6 31 5 5 11 4 10 26 12 6 16 8 2 4 28 www.cuidol.in Unit-2 (MBA602) All right are reserv1ed3with CU-IDOL

Expanding the Frequency Distribution 15  There are additional features that we can add to the frequency distribution that will provide a better understanding of the data  Midpoint,  Relative frequency,  Cumulative frequency  The midpoint of a class is the sum of the lower and upper limits of the class divided by two. The midpoint is sometimes called the class mark. Midpoint= Lower class limit Upper class limit 2 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

RELATIVE FREQUENCY 16  The relative frequency of a class is the portion or percent of the data that falls in that class. – To find the relative frequency of a class, divide the frequency, f, by the sample size, n. Relative Frequency = Class Frequency f Sample Size n Note: Relative frequency can be written as a decimal or as a percent.  The cumulative frequency of a class is the sum of the frequency for that class and all previous classes. – The cumulative frequency of the last class is equal to the sample size. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Example: Midpoints, Relative and Cumulative 17 Frequencies  Using the frequency distribution, find Class Frequency, f the midpoint, relative frequency, and 7 – 18 6 cumulative frequency. 19 – 30 10 31 – 42 13 43 – 54 8 55 – 66 5 67 – 78 6 79 – 90 2 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Solution: Midpoints, Relative and 18 Cumulative Frequencies Expanded Frequency Distribution Class Frequency, Midpoint Relative Cumulative 7 – 18 6 12.5 frequency frequency 19 – 30 10 24.5 31 – 42 13 36.5 0.12 6 43 – 54 8 48.5 0.20 16 55 – 66 5 60.5 0.26 29 67 – 78 6 72.5 0.16 37 79 – 90 2 84.5 0.10 42 0.12 48 www.cuidol.in 0.04 50 Σf = 50  f 1 n Unit-2 (MBA602) All right are reserved with CU-IDOL

Example: Midpoints, Relative and Cumulative 19 Frequencies  Using the frequency distribution, find the Class Frequency, f midpoint, relative frequency, and cumulative 0 – 10 5 frequency. 11 – 21 13 22 – 32 16 33 – 43 7 44 – 54 11 55 – 65 3 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

Solution: Midpoints, Relative and 20 Cumulative Frequencies Expanded Frequency Distribution Class Frequency, f Midpoin Relative Cumulative t Frequency Frequency 0 – 10 27 11 – 21 13 5 0.3506 27 22 – 32 16 16 0.1688 40 33 – 43 7 27 56 44 – 54 11 38 0.2078 63 55 – 65 3 49 74 Σ f = 50 0.0909 60 0.1429 77 0.0390 Σ≈1 www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

GRAPHS 21 Group Data Ungroup Data For Continuous data or quantitative  Line graphs variables:  Bar Chart The three commonly used graphic forms are  Pie Chart  Histograms  Frequency Polygons  Cumulative Frequency Curve. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

HISTOGRAM 22 A Histogram is a graph in which the class midpoints or limits are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

FREQUENCY POLYGONS 23  A Frequency Polygon consists of line segments connecting the points formed by the class midpoint and the class frequency. Frequency 10 8 6 4 2 0 12 16 20 24 26 Class Midpoint www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

CUMULATIVE FREQUENCY CURVE 24 A curve that represents the cumulative frequency distribution of grouped data on a graph is called a Cumulative Frequency Curve or an Ogive. Representing cumulative frequency data on a graph is the most efficient way to understand the data and derive results. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

BAR CHART 25 Student’s Living Area 30NUMBER OF STUDENT 25 17 25 Sukrabad 12 20 15 7 Mohammadpur Dhanmondi 10 Mirpur Unit-2 (MBA602) AREA 5 0 All right are reserved with CU-IDOL www.cuidol.in

LINE GRAPHS 26 % of Education by Year In Bangladesh 5 8 17 22 29 13 15 32 12 25 38 17 19 19 33 41 1990 1995 27 2010 5 8 23 22 2015 13 15 32 29 Female 17 19 2000 2005 33 38 Male 12 17 41 Total 19 25 23 27 Total Male Female www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

PIE CHART 27 DIU Student CSE EEE BBA Others CSE 28% Others 44% www.cuidol.in BBA EEE 11% 17% Unit-2 (MBA602) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 1) Total relative frequency is always 28 a. One b. Half c. Quarter d. Two 2) The graph which shows the changes over a specific time period is called a. meridian graph b. pie graph c. line graph d. bar graph 3) Considering the line graph, the y-axis represents a. time period in years b. subject of measurement c. time period in days d. time period in minutes 4) The vertical axis of bar graph is also known as a. y-axis b. h-axis c. v-axis d. x-axis Answers: 1.(a) , 2.(c) , 3. (b) , 4. (a) www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

SUMMARY  The graphs showing the relationships of various parameters or variables are easily perceptible to the mind of the2 9 analyser or decision maker. The graphs can be gainfully used to chart the frequency distribution information under the details of the data in a concise manner. There are following types of graphs for presenting the frequency distribution: 1. Histograms 2. Frequency Polygon 3. Frequency Curves 4. Ogives, also commonly called Cumulative Frequency Curves  A table that shows classes or intervals of data with a count of the number of entries in each class. It is used to organize data and helps to recognize patterns is called frequency distribution.  A curve that represents the cumulative frequency distribution of grouped data on a graph is called a Cumulative Frequency Curve or an Ogive. Representing cumulative frequency data on a graph is the most efficient way to understand the data and derive results. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

FREQUENTLY ASKED QUESTIONS 30 Q1. . How can be graph used? Ans: . The graphs can be gainfully used to chart the frequency distribution information under the details of the data in a concise manner. For further details Refer to the SLM. Q2. Name the different types of graphs. Ans: There are following types of graphs for presenting the frequency distribution: 1. Histograms 2. Frequency Polygon 3. Frequency Curves 4. Ogives, also commonly called Cumulative Frequency Curves For further details Refer to the SLM. Q3. What is Histogram? Ans: A graph of a data set, in the form of series of rectangles, width indicating the class interval and height as its frequency. For further details Refer to the SLM www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

REFERENCES 31  Black, K. (2008). Business statistics for contemporary decision making. New Delhi: Wiley India.  Schiller, J., Srinivasan, R.,Spiegel, Schaum's.M(2012)..Outline Of Probability and Statistics. New Delhi: McGraw-Hill.  Levin, R. I.,Rubin, D. S.(1999). Statistics for management. New Delhi: Prentice Hall of India.  Webster, A. (2006). Applied statistics for business and economics. New Delhi: McGraw Hill. www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL

32 THANK YOU For queries Email: [email protected] www.cuidol.in Unit-2 (MBA602) All right are reserved with CU-IDOL