module 3 lecture notes

MODULE 3:DESCRIPTIVE STATISTICS

04/13/23 BUS216: Probability & Statistics for Economics & Business 1

Descriptive Statistics• Population parameter: a number calculated from all the

population measurements that describes some aspect of the population

• Sample statistic: a number calculated using the sample measurements that describes some aspect of the sample

• Interval or Ratio level data

• Make inferences about populations

• Describe the variable of interest

04/13/23 2

Descriptive Statistics

• Measures of Central Tendency

• Mean, Median, Mode, Percentiles

• Measures of Variation

• Range, IQR, MAD, Variance, Standard Deviation, Coefficient of

Variation

• Measures of Shape

• Skewness, Box and Whisker Plot, Outliers

• Measures of Location

• Z score or Standard Score

04/13/23 3

Measures of Central Tendency

04/13/23 4

Measures of Central Tendency• Percentiles, Deciles, Quartiles

• For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements fall at or below the value and (100-p) percent of the measurements fall at or above the value

• The first quartile Q1 is the 25th percentile • The second quartile (median) is the 50th percentile• The third quartile Q3 is the 75th percentile• The interquartile range IQR is Q3 - Q1

04/13/23 BUS216 Module 3 5

Percentiles

04/13/23 6

Measures of Variation

04/13/23 7

Descriptions of the spread or dispersion of a set of data.

Measures of Variation

04/13/23 8

Measures of Variation

04/13/23 BUS216 Module 3 9

Measures of Variation

04/13/23 BUS216 Module 3 10

Measures of Variation

04/13/23 BUS216 Module 3 11

Measures of Variation

04/13/23 BUS216 Module 3 12

Measures of Shape

04/13/23 13

Measures of Shape

04/13/23 BUS216 Module 3 14

Measures of Shape

04/13/23 BUS216 Module 3 15

Measures of Shape

04/13/23 BUS216 Module 3 16

Measures of Shape

The “Box” in the plot ….

04/13/23 BUS216 Module 3 17

Hinge Hinge

Median

Measures of Location

04/13/23 BUS216 Module 3 18

Normal Populations: Empirical Rule

Empirical Rule

•68% of the population measurements lie within

one standard deviation of the mean

•95% of the population measurements lie within

two standard deviations of the mean

•99.7% of the population measurements lie within

three standard deviations of the mean

04/13/23 BUS216 Module 3 19

04/13/23 20

Non-Normal Populations: Chebychev’s Theorem

04/13/23 21

Computer Applications

Descriptive Statistics: Price

Variable Mean StDev Variance CoefVar Minimum Q1 Median Q3

Price 98.03 57.96 3359.38 59.12 1.00 42.50 98.00 149.75

N for

Variable Maximum Range IQR Mode Mode Skewness

Price 199.00 198.00 107.25 10, 16, 38, 148 4 -0.03

The data contain at least five mode values. Only the smallest four are shown.

04/13/23 BUS216 Module 3 22