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# Measures of variation. Week 4 (1)

## 1. BBA182 Applied Statistics Week 4 (1)Measures of variation

DR SUSANNE HANSEN SARALEMAIL: [email protected]

HT TPS://PIAZZA.COM/CLASS/IXRJ5MMOX1U2T8?CID=4#

WWW.KHANACADEMY.ORG

DR SUSANNE HANSEN SARAL

1

## 2. Numerical measures to describe data

Describing Data NumericallyCentral Tendency

Variation

Mean

Quartile

Median

Range

Mode

Interquartile Range

Variance

Standard Deviation

Coefficient of Variation

COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-2

## 3. Interquatile range, IQR

Alternative way to calculate the IQRKhan Academy

## 4.

## 5. Five-Number Summary of a data set

In describing numerical data, statisticians often refer to thefive-number summary. It refers to five the descriptive

measures we have looked at:

minimum value

first quartile

median

third quartile

maximum value

minimum < Q1 < median < Q3 < maximum

It gives us a good idea where the data is located and how it is spread in the

data set

DR SUSANNE HANSEN SARAL

## 6. Five-Number Summary: Example

Sample Ranked Data:minimum <

6

6 7 8 9 10 11

Q1 < median <

< 7.75 < 10.5

Q3

11 12

< maximum

< 12.25 <

DR SUSANNE HANSEN SARAL

13 14

14

## 7. Exercise

Consider the data given below:110

a.

b.

c.

d.

e.

f.

g.

125

99

115

119 95 110

Compute the mean.

Compute the median.

What is the mode?

What is the shape of the distribution?

What is the lower quartile, Q1?

What is the upper quartile, Q3?

Indicate the five number summary

132

85

## 8. Exercise

Consider the data given below.85

95

99

110

110

115

119

125

132

a.

Compute the mean. 110

b.

Compute the median. 110

c.

What is the mode? 110

d.

What is the shape of the distribution? Symmetric, because mean = median=mode

e.

What is the lower quartile, Q1? 97

f.

What is the upper quartile, Q3? 122

g.

Indicate the five number summary 85 < 97 < 110 < 122 < 132

## 9. Five number summary and Boxplots

Boxplot is created from the five-number summaryA boxplot is a graph for numerical data that describes the shape of

a distribution, in terms of the 5 number summary.

It visualizes the spread of the data in the data set.

COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-9

## 10. Five number summary and Boxplots

Boxplot is created from the five-number summaryThe central box shows the middle half of the data from Q1 to Q3,

(middle 50% of the data) with a line drawn at the median

Two lines extend from the box. One line is the line from Q1 to the

minimum value, the other is the line from Q3 to the maximum value

A boxplot is a graph for numerical data that describes the shape of a

distribution, like the histogram

COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-10

## 11. Five number summary and boxplot

1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5Minimum number = 1

Maximum number = 5