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Mathematics

Find the mean and the median of all the (positive) factors of 48.

Statistics

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Answer

Positive factors of 48 :

1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

By formula,

Mean=Sum of positive factors of 48No. of factors\text{Mean} = \dfrac{\text{Sum of positive factors of 48}}{\text{No. of factors}}

Sum of positive factors of 48 = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124.

Mean =12410=12.4= \dfrac{124}{10} = 12.4

Here, n = 10 which is even.

By formula,

Median = n2th observation+(n2+1)th observation2\dfrac{\dfrac{n}{2}\text{th observation} + \Big(\dfrac{n}{2} + 1\Big)\text{th observation}}{2}

Substituting the values we get,

Median=102th observation+(102+1)th observation2=5th observation + 6th observation2=6+82=142=7\text{Median} = \dfrac{\dfrac{10}{2}\text{th observation} + \Big(\dfrac{10}{2} + 1\Big)\text{th observation}}{2} \\[1em] = \dfrac{\text{5th observation + 6th observation}}{2} \\[1em] = \dfrac{6 + 8}{2} \\[1em] = \dfrac{14}{2} \\[1em] = 7

Hence, mean = 12.4 and median = 7.

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