Business Statistics Chapter 2 Charts & Graphs by Ken Black

Learning Objectives Recognize the difference between grouped and ungrouped data Construct a frequency distribution Construct a histogram, a frequency polygon, an ogive, a pie chart, a stem and leaf plot, a Pareto chart, and a scatter plot 2

Ungrouped Versus Grouped Data Ungrouped data have not been summarized in any way are also called raw data Grouped data have been organized into a frequency distribution 7

Example of Ungrouped Data 42 30 53 50 52 55 49 61 74 26 58 40 28 36 33 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54 Ages of a Sample of Managers from Tata Company in India 8

Frequency Distribution of Tata company Manager’s Ages Class Interval Frequency 20-under 30 6 30-under 40 18 40-under 50 11 50-under 60 11 60-under 70 3 70-under 80 1 9

Data Range Smallest Largest 42 30 53 50 52 55 49 61 74 26 58 40 28 36 33 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54 Smallest Largest 10

Number of Classes and Class Width The number of classes should be between 5 and 15. Fewer than 5 classes cause excessive summarization. More than 15 classes leave too much detail. Class Width Divide the range by the number of classes for an approximate class width Round up to a convenient number 11

Class Midpoint 12

Relative Frequency Relative Class Interval Frequency Frequency 20-under 30 6 .12 30-under 40 18 .36 40-under 50 11 .22 50-under 60 11 .22 60-under 70 3 .06 70-under 80 1 .02 Total 50 1.00 13

Cumulative Frequency Cumulative Class Interval Frequency Frequency 20-under 30 6 6 30-under 40 18 24 40-under 50 11 35 50-under 60 11 46 60-under 70 3 49 70-under 80 1 50 Total 50 14

Class Midpoints, Relative Frequencies, and Cumulative Frequencies Relative Cumulative Class Interval Frequency Midpoint Frequency Frequency 20-under 30 6 25 .12 6 30-under 40 18 35 .36 24 40-under 50 11 45 .22 35 50-under 60 11 55 .22 46 60-under 70 3 65 .06 49 70-under 80 1 75 .02 50 Total 50 1.00 15

Cumulative Relative Frequencies Relative Cumulative Relative Class Interval Frequency Frequency Frequency Frequency 20-under 30 6 .12 6 .12 30-under 40 18 .36 24 .48 40-under 50 11 .22 35 .70 50-under 60 11 .22 46 .92 60-under 70 3 .06 49 .98 70-under 80 1 .02 50 1.00 Total 50 1.00 16

Common Statistical Graphs Histogram -- vertical bar chart of frequencies Frequency Polygon -- line graph of frequencies Ogive -- line graph of cumulative frequencies Pie Chart -- proportional representation for categories of a whole Stem and Leaf Plot Scatter Plot 17

Histogram Class Interval Frequency 20-under 30 6 30-under 40 18

Histogram Construction Class Interval Frequency 20-under 30 6 30-under 40 18 40-under 50 11 50-under 60 11 60-under 70 3 70-under 80 1 19

Frequency Polygon Class Interval Frequency 20-under 30 6

Ogive Cumulative Class Interval Frequency 20-under 30 6 30-under 40 24 21

Relative Frequency Ogive Cumulative Relative Class Interval Frequency 20-under 30 .12 30-under 40 .48 40-under 50 .70 50-under 60 .92 60-under 70 .98 70-under 80 1.00 22

Safety Examination Scores for Plant Trainees Raw Data Stem Leaf 2 3 4 5 6 7 8 9 3 9 7 9 5 6 9 0 7 7 8 8 0 2 4 5 5 6 7 7 8 9 1 1 2 3 3 6 8 9 1 1 2 4 7 86 76 23 77 81 79 68 92 59 75 83 49 91 47 72 82 74 70 56 60 88 97 39 78 94 55 67 89 28

Construction of Stem and Leaf Plot Raw Data Stem Leaf 2 3 4 5 6 7 8 9 3 9 7 9 5 6 9 0 7 7 8 8 0 2 4 5 5 6 7 7 8 9 1 1 2 3 3 6 8 9 1 1 2 4 7 86 76 23 77 81 79 68 92 59 75 83 49 91 47 72 82 74 70 56 60 88 97 39 78 94 55 67 89 Stem Leaf Stem Leaf 29

Scatter Plot Registered Vehicles (1000's) Gasoline Sales (1000's of Gallons) 5 60 15 120 9 90 140 7

A X company surveyed age of 53 of its middle level managers A X company surveyed age of 53 of its middle level managers. Which has later been organised into frequency distribution as shown below. Determine the class midpoint, relative frequency & Cum. R.F for these data. Compute a histogram, frequency polygon, Ogive & Pie chart for the same. CI F 20-25 8 25-30 6 30-35 5 35-40 12 40-45 15 45-50 7

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