Displaying Summarizing Data Lesson 02 A From Data

Displaying & Summarizing Data (Lesson – 02 A) From Data to Information Dr. C. Ertuna 1

Displaying & Summarizing Data What do these data tell us about CPI? Dr. C. Ertuna 2

Displaying & Summarizing Data • Raw data need to be converted into useful managerial information • Visual Displays and Statistical Summaries are means to convert raw data into insightful information. • That information could be interpreted for decision making purposes Dr. C. Ertuna 3

Visual Display of Data Dr. C. Ertuna 4

Displaying & Summarizing Data • Raw data need to be converted into useful managerial information • Visual Displays and Statistical Summaries are means to convert raw data into insightful information. • That information could be interpreted for decision making purposes Dr. C. Ertuna 5

Displaying & Summarizing Data • CPI increased steadily over the last two years. • Over the last 6 months, however, that increase slowed down. Dr. C. Ertuna 6

Displaying & Summarizing Data • CPI increased steadily over the last two years. • Over the last 6 months, however, that increase slowed down. Dr. C. Ertuna 7

Graphical Display Methods • Charts (Column, Bar, Line, Pie, Area) and Scatter Diagrams make it easier to gain insights about the data (visual interpretation of data), • They provide also excellent communication vehicles • The drawback is that data could be distorted by manipulating the scale on the chart. Dr. C. Ertuna 8

Creating a Column Chart 1. Enter data in the worksheet 2. Select Chart Wizard 3. Select Clustered Column Chart (1: 1) 4. Select Data Range (including Labels) 5. Select “Series Rows” 6. Select Finish Data: St-CE-Ch 02 -x 1 -Examples-Slide Dr. C. Ertuna 9

Statistical Summaries • Descriptive Statistics such as – Measures of Central Tendency (mean, median, mode, midrange, etc. ) – Measures of Dispersion (range, variance, standard deviation, etc. ) – Frequency Distributions – Histograms • Statistical Relationships (such as Correlation) provide effective way of obtaining meaningful information from data. Dr. C. Ertuna 10

Descriptive Statistics • Descriptive statistics need to be computed for both the sample and the population • “Population Parameters” is the name for the Descriptive Statistics for population Greek letters represent Population Parameters • “Sample Statistics” is the name for the Descriptive statistics for sample Roman letters represent Sample Statistics. Dr. C. Ertuna 11

Measure of Central Tendency Blood pressures for North American and other managers are given on the left. Which group has higher blood pressure? To answer this question we need to measure first, the central tendency of each group. Data: St-CE-Ch 02 -x 1 -Examples-Slide 13 Dr. C. Ertuna 12

Descriptive Measures of C. T. Descriptive Measure Computation Method Data Level Pros/Cons Mean Sum of values divided by the number of values Ratio Interval • Numerical center of the data • Sum of the deviations from the mean is zero • Sensitive to extreme values Median Middle value for data that have been sorted Ratio Interval Ordinal • Not sensitive to extreme values • Computed only for the central values • Does not use information from all the data Mode Value(s) that occur most frequently in the data Ratio • May not reflect the center Interval • May not exist Ordinal • Might have multiple modes Nominal Dr. C. Ertuna 13

Descriptive Measures of C. T. Descriptive Measure Mean Median Mode Excel Command =Average(Range) =Median(Range) =Mode(Range) Symbol , Pros/Cons • Numerical center of the data • Sum of the deviations from the mean is zero • Sensitive to extreme values • Not sensitive to extreme values • Computed only for the central values • Does not use information from all the data • May not reflect the center • May not exist • Might have multiple modes Dr. C. Ertuna 14

Example: Measure of C. T. (cont. ) Data: St-CE-Ch 02 -x 1 -Examples-Slide 13 Blood pressures for NA and other managers are given on the left. 1. Compare mean, median, mode and midrange. 2. Explain the meaning of the results. 3. Evaluate the implications. Dr. C. Ertuna 15

Example: Measure of C. T. (cont. ) Data: St-CE-Ch 02 -x 1 -Examples-Slide 13 Dr. C. Ertuna 16

Example: Measure of C. T. (cont. ) Data: St-CE-Ch 02 -x 1 -Examples-Slide 13 Dr. C. Ertuna 17

Checking on the Extreme Value • Before we can relay on the mean as a “good” measure for central tendency we need to test for extreme values. • One such measure is the 3 -sigma rule. • The standard deviation of a series is computed then multiplied by 3 and the result is: (a) once added to the mean to find the Upper Limit for extreme value detection and (b) once deducted from the mean value to determine the Lower Limit. Dr. C. Ertuna 18

Example: Checking on Extreme Value Dr. C. Ertuna 19

Example: Measure of C. T. (cont. ) Blood pressure statistics for NA and other managers are given on the left. 1. Compare mean, median, mode. 2. Explain the meaning of the results. 3. Evaluate the implications. Dr. C. Ertuna 20

Note: Comparison of the Means • Actually To compare the means of two series we need to run a hypothesis test (two sample mean test – t-test). • We will learn how to run hypothesis tests, later. • For now we will do a simple face value comparison with the knowledge that the true comparison requires a formal test. Dr. C. Ertuna 21

Comparison: Measure of C. T. (cont. ) • Mean, Median, and Mode of NAmanagers are greater than “Other” managers • Median is slightly higher than the mean for the NA managers and the opposite is true for others. Dr. C. Ertuna 22

Meaning: Measure of C. T. (cont. ) 1 Mean values suggests that blood pressures of NA-managers are higher than the “other” managers 2 Midrange could be interpreted as a raw measurement for the effect of distortion by the extreme values on the mean. It suggests that the real mean for NA is under estimated and for “Others” it is pretty much accurate. Dr. C. Ertuna 23

Meaning: Measure of C. T. (cont. ) 3 Half of the NA managers have higher blood pressure than the mean. Median values support point 2 for NA and suggests that mean for “Others” may overestimate the central tendency 4 Mode values reveal that most observed numbers are below the mean for NA and above for “Others. ” Dr. C. Ertuna 24

Evaluation: Measure of C. T. (cont. ) • High blood pressure is an indicator for stress and strain • The results suggest that the North American managers of the company are under much more stress than the managers of the company in the other parts of the world • If corrective measures are not taken than Errors, Loss of Managerial Talent, etc. may occur in NA. Dr. C. Ertuna 25

Next Lesson (Lesson – 02 B) Measure of Dispersion Dr. C. Ertuna 26