Question

Find the mean and median of all the positive factors of 72.

Answer 1

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`[ 6^th term + 7^th term ]

= `1/2`[ 8 + 9 ]

= `1/2` x 17
= 8.5