MeasureMeasure of of Central TendencyCentral TendencyLesson 1 (5Lesson 1 (5thth 6 Weeks) 6 Weeks)

TEKS TEKS 6.10B6.10B

RangeRange

• The The differencedifference between the between the greatestgreatest and and leastleast numbers in a set numbers in a set of of datadata

• EX: 89, 82, 79, 74, 69, 67, 58, 56, 54EX: 89, 82, 79, 74, 69, 67, 58, 56, 5489 is the greatest number54 is the least numberTheir difference is 89-54 or 35.The range of this data is 35.

MedianMedian

• Middle numberMiddle number of a set of data, of a set of data, when the numbers are in when the numbers are in numericalnumerical order. If there are order. If there are twotwo middle numbers, the middle numbers, the meanmean (average) of the two numbers is (average) of the two numbers is the median.the median.

Examples:Examples:

• Ex: 115, 108, 101, 92, 84, 84, 62Ex: 115, 108, 101, 92, 84, 84, 62

• Ex: 3, 8, 12, 35, 45, 61, 78, 81Ex: 3, 8, 12, 35, 45, 61, 78, 81

92 is in the middle & is the median.

There are two middle numbers, 35 & 45.

Find the number halfway between 35 & 45.

4535

+80

2 804

-80

0

40 is the middle number or the median of this set of data.

ModeMode

• Number that Number that occurs mostoccurs most oftenoften in a in a set of dataset of data

• EX: 45, 450, 450, 465, 465, 465, 470EX: 45, 450, 450, 465, 465, 465, 470

465465 occurs the most & is the occurs the most & is the modemode

MeanMean

• An An averageaverage of the values in a set of of the values in a set of datadata

• Useful when there are no Useful when there are no outliersoutliers

• If the values of a group of data is If the values of a group of data is evenedevened outout so all the values are the so all the values are the same, the evened-out number is the same, the evened-out number is the meanmean

• Another procedure to find the Another procedure to find the meanmean is to is to dividedivide the the sumsum of the values by of the values by the the numbernumber of values in the set ( of values in the set (addadd & & dividedivide))

• EX: 4 + 7 + 3 + 4 + 13 + 3 + 7 + 13 EX: 4 + 7 + 3 + 4 + 13 + 3 + 7 + 13 ==

54 ÷ 8 = the mean is54 ÷ 8 = the mean is

54

6.75

6.75

Example:Example:

• Lisbeth scores for her last mini-Lisbeth scores for her last mini-assessment are listed below. Find the assessment are listed below. Find the range, median, mode and mean of her range, median, mode and mean of her last mini-assessment scores.last mini-assessment scores.

85, 90, 95, 80, 73, 72, 100, 8085, 90, 95, 80, 73, 72, 100, 80

• First things first, let’s place the scores First things first, let’s place the scores in order from in order from leastleast to to greatestgreatest..

72, 73, 80, 80, 85, 90, 95, 72, 73, 80, 80, 85, 90, 95, 100100

• Range:Range:

• Median:Median:

100- 72

28

9 10

Range is 28

72, 73, 80, 80, 85, 90, 95, 10072, 73, 80, 80, 85, 90, 95, 100

80 & 85 are both in the middle.

We need to add & divide.

72, 73, 80, 80, 85, 90, 95, 72, 73, 80, 80, 85, 90, 95, 100100

80+ 85165

16528

-1605

2

- 41

0.

0

5

-100

The median is

82.5.

• Mode:Mode:The number we see the most is 80. So the mode is 80.

72, 73, 80, 80, 85, 90, 95, 72, 73, 80, 80, 85, 90, 95, 100100

• MeanMean

72, 73, 80, 80, 85, 90, 95, 72, 73, 80, 80, 85, 90, 95, 100100

7273

8080

9085

+ 100

95

5

1

67

67588

-6435

4

-323

0.

0

3

-246

0

0

7

-564

The mean is 84.375.

0

0

5

-400