Question

The median of the data 13, 15, 16, 17, 19, 20 is: (a)30/2 (b)31/2 (c)33/2 (d)35/2

Answer 1

Answer: option (c)

Hope it helps.......

Answer 2

Given:

A data 13, 15, 16, 17, 19, 20.

To find:

The median of the given data.

Solution:

As we know that if there is an odd number (n) of observations in a data, then its median is obtained by:

$( \frac{n + 1}{2} )th \: observation$

Also,

if there is an even number (n) of observations in a data, then median is obtained by:

$\frac{ (\frac{n}{2})th \: observation \: + (\frac{n}{2} + 1)th \: observation }{2}$

Now,

as given, we have,

A data

13, 15, 16, 17, 19, 20

As we can see, there are 6 observations in the given data set.

So,

n = 6, which is even

So,

$\frac{n}{2} th \: observation \: = \frac{6}{2} = 3rd \: observation$

3rd observation = 16

Also,

$(\frac{n}{2} + 1)th \: observation \: = \:( 3 + 1)th \: observation \: = \: 4th \: observation$

4th observation = 17

So,

the median is

$= \frac{16 + 17}{2}$

$= \frac{33}{2}$

Hence, the median of the data is (c) 33/2.