Chapter 3: intoduction to statistics the Statistical Process


Mean, median and Mode for Grouped frequency distribution



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Mean, median and Mode for Grouped frequency distribution



  • Mean, where; =class midpoint

(Student must show the working ie. Find midpoint and )

  • Median :

- find cumulative frequency

- find location of median class =

- Median :

Where; =lower boundary of the median class



= cumulative frequency until the point L (before median class)

= frequency of the median class

c =class width of median class

  • Mode :

- find location of modal class : class with the largest frequency

-Mode



where; =lower boundary of the modal class

a = different between frequencies of modal class and the class before it.

b= different between frequencies of modal class and the class after it.

c =class width of median class

Example:

  1. These numbers of books were read by each of the 28 students in a literature class. Find mean, median and mode.

Number of books

Frequency

0 – 2

2

3 – 5

6

6 – 8

12

9 – 11

5

12 – 14

3



  1. Eighty randomly selected light bulbs were tested to determine their lifetimes (in hours). This frequency distribution was obtained. Find mean, median and mode.

Class Boundaries

Frequency

52.5 – 63.5

6

63.5 – 74.5

12

74.5 – 85.5

25

85.5 – 96.5

18

96.5 – 107.5

14

107.5 – 118.5

5

3.3.2 MEASURES OF VARIATION

Variance and Standard deviation (the spread of data set)

Group A

Group B

80

55

81

88

82

100

=81

=81

Variation, s2 =1

Variation, s2 =543


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