Question

Find the Median of the scores 15,17,19,21,23,25.​

Answer 1

Median of the scores 15 , 17 , 19 , 21 , 23 , 25 is 20

Given :

The scores 15 , 17 , 19 , 21 , 23 , 25

To find :

Median of 15 , 17 , 19 , 21 , 23 , 25

Concept :

Median :

Median is the middle most value of a set of observations when the samples are arranged in order of magnitudes ( Either in ascending or in descending)

Formula for calculating median :

1. If total number of observations n is odd then

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

2. If total number of observations n is even then

$\displaystyle \sf{ Median = \frac{1}{2} \times \bigg[ {\bigg( \frac{n }{2} \bigg)}^{th} \: observation +{\bigg( \frac{n}{2} + 1 \bigg)}^{th} \: observation \bigg] }$

Solution :

Step 1 of 3 :

Write down the given scores

Here the given scores are 15 , 17 , 19 , 21 , 23 , 25

Step 2 of 3 :

Rearrange in ascending order

Rearranging in ascending order we get

15 , 17 , 19 , 21 , 23 , 25

Step 3 of 3 :

Find the median of the scores

Number of observations = 6 which is even

Therefore the required median

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {\bigg( \frac{n }{2} \bigg)}^{th} \: observation +{\bigg( \frac{n}{2} +1 \bigg)}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {\bigg( \frac{6 }{2} \bigg)}^{th} \: observation +{\bigg( \frac{6}{2} + 1 \bigg)}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {3}^{rd} \: observation +{4}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times (19 + 21) }$

$\displaystyle \sf{ = \frac{1}{2} \times 40 }$

$\displaystyle \sf{ = 20 }$

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Answer 2

The median is 20.

Arrange given data in ascending order

15,17,19,21,23,25.

Here there even number of digits on data.

So median = average of n/2 th observation and (n/2 + 1)th observation

= (19+21 ) /2

= 40/2

= 20

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