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Question
Find the mean and median of all the positive factors of 72.
Solution
Let us find the factors of 72:
72 = 1 x 72
= 2 x 36
= 3 x 24
= 4 x 18
= 6 x 12
= 8 x 9
= 9 x 8
= 12 x 6
= 18 x 4
= 24 x 3
= 36 x 2
= 72 x 1
Therefore, the data set is: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Mean of the above data set = `[ 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72 ]/12`
= `195/12`
= 16.25
Since the number of observation is 12, which is even,
median is given by
Median = `1/2[ (n/2)^"th" "term" + ( n/2 + 1 )^"th" "term" ]`
= `1/2[ (12/2)^"th" "term" + ( 12/2 + 1)^"th" "term" ]`
= `1/2`[ 6th term + 7th term ]
= `1/2`[ 8 + 9 ]
= `1/2` x 17
= 8.5
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