Measures of Central Tendency And

Variation

Mean◦ Average◦ The sum of the numbers divided by the number of

numbers◦ Represented by x

Median◦ Middle number of the ordered numbers from least

to greatest◦ Mean of middle two numbers

Mode◦ The number or numbers that occur most frequently◦ There may be one mode, no mode, or more than

one mode.

Measures of Central Tendency

Range◦ Difference between the greatest and the least values.

Quartiles◦ Values that separate the data into four equal subsets, each

containing one fourth of the data. Lower Quartile

◦ It divides the lower half of the data into two equal parts. Upper Quartile

◦ It divides the upper half of the data into two equal parts. Interquartile Range (IQR)

◦ Difference between the upper and lower quartiles Outlier

◦ A value that is much less or much greater than the rest of the data.◦ Any element of a set of data that is at least 1.5 interquartile ranges

less than the lower quartile or greater than the upper quartile.

Measures of Variation

1 1 2 4 6 7 7 8 9 10 12 13 17 17 18

Measures of Variation

1 1 2 4 6 7 7 8 9 10 12 13 17 17 18

Measures of Variation

median

1 1 2 4 6 7 7 8 9 10 12 13 17 17 18

Measures of Variation

median

Lower Quartile (LQ)

1 1 2 4 6 7 7 8 9 10 12 13 17 17 18

Measures of Variation

median

Lower Quartile (LQ)

Upper Quartile (UQ)

1 1 2 4 6 7 7 8 9 10 12 13 17 17 18

Measures of Variation

median

Lower Quartile (LQ)

Upper Quartile (UQ)

UQ – LQ = IQR

1 8 9 10 10 11 12 13 13 15 27

Outlier

1 8 9 10 10 11 12 13 13 15 27

Outlier

Median

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ UQ

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ UQ

IQR = 13 – 9 = 4

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ UQ

IQR = 13 – 9 = 4

9 – 1.5(4) = 3

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ UQ

IQR = 13 – 9 = 4

9 – 1.5(4) = 3

Outlier

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ UQ

IQR = 13 – 9 = 4

9 – 1.5(4) = 3

Outlier

13 + 1.5(4) = 19

1 8 9 10 10 11 12 13 13 15 27

Outlier

MedianLQ UQ

IQR = 13 – 9 = 4

9 – 1.5(4) = 3

Outlier

13 + 1.5(4) = 19

Outlier

Average Monthly High Temperatures (°F)

Month Honolulu

January 80.1

February 80.5

March 81.6

April 82.8

May 84.7

June 86.5

July 87.5

August 88.7

September 88.5

October 86.9

November 84.1

December 81.2

Find Measures of Central Tendency and Variation

Mean 80.1 + 80.5 + 81.6 + 82.8 + 84.7 + 86.5 + 87.5 + 88.7 + 88.5 + 86.9 + 84.1 +

81.2 12

1013.1 12

84.425

Find Measures of Central Tendency and Variation

Median80.1, 80.5, 81.2, 81.6, 82.8, 84.1, 84.7, 86.5, 86.9, 87.5, 88.5, 88.7

84.1 and 84.7

84.1 + 84.7 2

168.8 2

84.4

Find Measures of Central Tendency and Variation

ModeNo mode

Range88.7 – 80.1 = 8.6

Find Measures of Central Tendency and Variation

80.1, 80.5, 81.2, 81.6, 82.8, 84.1, 84.7, 86.5, 86.9, 87.5, 88.5, 88.7

Lower Quartile 81.2 + 81.6 = 162.8

162.8 ÷ 2 = 81.4

Upper Quartile86.9 + 87.5 = 174.4

174.4 ÷ 2 = 87.2

Find Measures of Central Tendency and Variation

IQR87.2 – 81.4 = 5.8

Outlier 81.4 – 1.5(5.8) = 72.7

87.2 + 1.5(5.8) = 95.9

No outliers

Find Measures of Central Tendency and Variation

Find the measures of central tendency and variation for the information in the table.

Guided Practice

State Area (thousand square miles)

Connecticut 6

Delaware 2

Georgia 59

Maryland 12

Massachusetts 11

New Hampshire 9

New Jersey 9

New York 54

North Carolina 54

Pennsylvania 46

Rhode Island 2

South Carolina 32

Virginia 43

Guided Practice