Question

Determine the median of 24, 23, a, a-1, 12, 16 where a is the mean of 12, 16, 23, 24, 28, 29

Answer 1

$\huge\boxed{\mathtt\red{Solution\::-}}$

Given :-

• mean of 12, 16, 23, 24, 28 and 29 is a.

To Find :-

• median of 24, 23, a, a-1, 12, and 16.

Solving :-

⟹ mean of 12, 16, 23, 24, 28 and 29 is a.

⟹ no.of observation = 6 (even).

By Applying the formula :

$\large\boxed{\mathtt\blue{Mean=\frac{sum\:of\: observation}{no.of\: observation}}}$

✒ $\large{\mathtt{a=\frac{132}{6}}}$

✒ a = 22

$\large\boxed{\mathtt\green{∴a=22}}$

Now, finding the median :-

Observations :-

➽ 24, 23, a, a-1, 12, 16

→ 24, 23, 22, 21, 12, 16

→ 12, 16, 21, 22, 23, 24 (in order)

⟹ no. of observations = 6 (even)

Applying :-

$\large\boxed{\mathtt\blue{Median\:(even)=\frac{\frac{n+2}{2}+\frac{n}{2}}{2}\:th\: observation}}$

✒ $\large{\mathtt{Median = \frac{3rd+4th}{2}\:th}}$

✒ $\large{\mathtt{Median=\frac{21+22}{2}}}$

✒ Median = 43/2

$\large\boxed{\mathtt\green{∴Median=21.5}}$