Question

$\red {21}$
Find the median of all the factors of 144.​

Answer 1

Answer:

$\bold\red{Median=12}$

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Factors of 144 are given below:-

144 = 1 × 144

144 = 2 × 72

144 = 3 × 48

144 = 4 × 36

144 = 6 × 24

144 = 8 × 18

144 = 9 × 16

144 = 12 × 12

Factors = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 & 144.

Number of factors = 15[Odd number]

In odd number median is the middle number of the list.

So, median is the 8th number

=> Median = 12

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Answer 2

$\large{\underline{\underline{\mathfrak{\sf{\red{Answer-}}}}}}$

The Median of factors of 144 is 12.

$\large{\underline{\underline{\mathfrak{\sf{\red{Explanation-}}}}}}$

★ Factors of 144 :

$\sf{1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}$

★ Number of terms = 15 ( odd )

We know that,

$\large{\underline{\boxed{\mathfrak{\sf{\green{Median(odd)=(\dfrac{n+1}{2})^{th}\:term}}}}}}$

where, n is number of observations.

$\implies$ Median = $\sf{\dfrac{15+1}{2}^{th}\:term}$

$\implies$ Median = $\sf{\dfrac{16}{2}^{th}\:term}$

$\implies$ Median = $\sf{\cancel{{\dfrac{16}{2}}^{th}}}$ $\sf{term}$

$\implies$ Median = $\sf{{8}^{th}\:term}$

$\implies$ Median = 12

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