1. Statistics in Management
An introduction

2. Why a Manager Needs to Know about Statistics
To know how to properly present information
To know how to draw conclusions about populations based on sample information
To know how to improve processes
To know how to obtain reliable forecasts

3. The Growth and Development of Modern Statistics
Needs of government to collect data on its citizens
The development of the mathematics of probability theory
The advent of the computer

4. Key Definitions
A population (universe) is the collection of things under consideration
A sample is a portion of the population selected for analysis
A parameter is a summary measure computed to describe a characteristic of the population
A statistic is a summary measure computed to describe a characteristic of the sample

5. Population and Sample Inference on the population from the sample
Use statistics to summarize features
Use parameters to summarize features
Inference on the population from the sample

6. Descriptive statistics Inferential statistics
Statistical Methods
Descriptive statistics
Collecting and describing data
Inferential statistics
Drawing conclusions and/or making decisions concerning a population based only on sample data

7. Descriptive Statistics
Collect data
e.g. Survey
Present data
e.g. Tables and graphs
Characterize data
e.g. Sample mean

8. Inferential Statistics
Estimation
e.g.: Estimate the population mean weight using the sample mean weight
Hypothesis testing
e.g.: Test the claim that the population mean weight is 120 pounds
Drawing conclusions and/or making decisions concerning a population based on sample results.

9. Reasons for Drawing a Sample
Less time consuming than a census
Less costly to administer than a census

10. Simple Random Samples
Every individual or item from the frame has an equal chance of being selected
Selection may be with replacement or without replacement

11. Systematic Samples Decide on sample size: n
Divide frame of N individuals into groups of k individuals
Randomly select one individual from the 1st group
Select every k-th individual thereafter
N = 64
n = 8
k = 8
First Group

12. Coefficient of Variation
Summary Measures
Summary Measures
Central Tendency
Variation
Mean
Mode
Coefficient of Variation
Median
Range
Variance
Standard Deviation

13. Measures of Central Tendency
Average
Mode
Median

14. Arithmetic Mean Mean (arithmetic mean) of data values Sample mean
Population mean
Sample Size
Population Size

15. Arithmetic Mean The most common measure of central tendency
Affected by extreme values (outliers)
Mean = 5
Mean = 6

16. Median Robust measure of central tendency
Not affected by extreme values
In an ordered array, the median is the “middle” number
If n or N is odd, the median is the middle number
If n or N is even, the median is the average of the two middle numbers
Median = 5
Median = 5

17. Mode Value that occurs most often Not affected by extreme values
Used for either numerical or categorical data
There may be no mode
There may be several modes
No Mode
Mode = 9

18. Measures of Variation Variation Variance Standard Deviation
Coefficient of Variation
Range
Population
Variance
Population
Standard
Deviation
Sample
Variance
Sample
Standard
Deviation

19. Range Measure of variation
Difference between the largest and the smallest observations:
Range = = 5
Range = = 5

20. Variance Important measure of variation Shows variation about the mean
Sample variance:
Population variance:

21. Standard Deviation Most important measure of variation
Shows variation about the mean
Has the same units as the original data
Sample standard deviation:
Population standard deviation:

22. Comparing Standard Deviations
Data A
Mean = 15.5
s = 3.338
Data B
Mean = 15.5
s = .9258
Data C
Mean = 15.5
s = 4.57

23. Coefficient of Variation
Measures relative variation
Always in percentage (%)
Shows variation relative to mean
Is used to compare two or more sets of data measured in different units

24. Comparing Coefficient of Variation
Stock A:
Average price last year = $50
Standard deviation = $5
Stock B:
Average price last year = $100
Coefficient of variation: