Question

Find the median of the data 30, 25, 32, 23, 42, 36, 40, 33, 21, 43.​

Answer 1

★ How to do :-

Here, we are given with ten observations in which we are asked to find the mefian of those observations. So, first we should arrange all the observations (numbers) in ascending or descending order. Let's arrange them in ascending order. We have a methods in which we can solve for the median. We'll solve that method step by step for proper explanation. The formulas are given at last of the problem. So, let's solve!!

$\:$

➤ Solution :-

Ascending order :-

${\tt \leadsto 21, 23, 25, 30, 32, 33, 36, 40, 42, 43}$

Median :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{n}{2} + 1 \: \: th \: \: term}}}$

Substitute the value of n.

${\tt \leadsto \dfrac{10}{2} + 1}$

Simplify the fraction first.

${\tt \leadsto 5 + 1}$

Add the values.

${\tt \leadsto 6th \: \: term}$

We can see that the sixth term of ascending order is 33. So,

${\sf \leadsto \pink{\underline{\boxed{\sf Median = 33}}}}$

$\Huge\therefore$ The median of the data is 33.

━━━━━━━━━━━━━━━━━━━━━━

$\dashrightarrow$ Formulas of median :-

${\sf \to {Median}_{(Even \: observations)} = \dfrac{n}{2} + 1}$

${\sf \to {Median}_{(Odd \: observations)} = \dfrac{n + 1}{2}}$

In the formulas 'n' refers to number of observations.