Question

Find the median 79,81,89,81,78,82,84,76​

Answer 1

76,78,79,81,81,82,84,89

Answer 2

Given data:-

79, 81, 89, 81, 78, 82, 84, 76

Arranging in ascending order:-

76, 78, 79, 81, 81, 82, 84, 89

Solution:-

Here, Number of observations, N = 8 [even number]

So, formula for median:-

$\sf \large{Median} \: = \: \dfrac{ \bigg(\dfrac{n}{2} \bigg)^{th} + \: \bigg(\dfrac{n}{2} + 1 \bigg)^{th} \: observation}{2}$

$\sf \large{Median} \: = \: \dfrac{ \bigg(\dfrac{n}{2} \bigg)^{th} + \: \bigg(\dfrac{n}{2} + 1 \bigg)^{th} \: observation}{2} \\ \\ \sf \large{Median} \: = \: \dfrac{ \bigg(\dfrac{8}{2} \bigg)^{th} + \: \bigg(\dfrac{8}{2} + 1 \bigg)^{th} \: observation}{2} \\ \\ \sf \large{Median} \: = \dfrac{ \bigg(4 \bigg)^{th} + \bigg(\dfrac{8 + 2}{2} \bigg) ^{th} \: \: observation }{2} \\ \\ \sf \: \large{Median} \: = \: \dfrac{ \bigg(4 \bigg)^{th} + \bigg(5 \bigg)^{th} \: observation }{2} \\ \\ \sf \: \large{Median} \: = \dfrac{81 + 81}{2} \\ \\ \sf \: \large{Median} \: = \dfrac{162}{2} \\ \\ \sf \: \large{\boxed{\boxed{ \purple{\bf{Median = 81}}}}}$

Therefore, median of given data is 81 .

NOTE;-

If number of observations were odd, then formula used would be:-

$\sf \: median \: = \bigg(\dfrac{n + 1}{2} \bigg)^{th} observation$