Question

find the median 10,75,3,15,9,47,12,48,4,81,17,27​

Answer 1

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Observations are given as 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17 and 27.

Let us arrange them in ascending order,

3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75 and 81

Let us count the number of terms,

There are 12 terms.

In step 1, we have come to know that there are 10 terms,

So,

Applying the median formula,

When n is even, then, the median is given by,

There are 12 terms.

Let us count the number of terms,

$\begin{aligned}   & =\frac{1}{2}\left( {{\left( \frac{n}{2} \right)}^{th}}term+{{\left( \frac{n}{2}+1 \right)}^{th}}term \right) \\ & =\frac{1}{2}\left( {{\left( \frac{12}{2} \right)}^{th}}term+{{\left( \frac{12}{2}+1 \right)}^{th}}term \right) \\ & =\frac{1}{2}\left( {{6}^{th}}term+{{7}^{th}}term \right) \\ & =\frac{1}{2}\left( 15+17 \right) \\ & =\frac{32}{2} \\ & =16 \\ \end{aligned}$

The median is 16.

Answer 2

Answer:

Observations are given as 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17 and 27.

Let us arrange them in ascending order,

3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75 and 81

Let us count the number of terms,

There are 12 terms.

In step 1, we have come to know that there are 10 terms,

So,

Applying the median formula,

When n is even, then, the median is given by,

There are 12 terms.

The median is 16.