Question

Find the median of 17,2,7, 27,15,5,14,8,,10,24,48,10,8,7,18,28

Answer 1

221.75 is the mean of this.

Answer 2

Median of 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28 is 12

Given :

The numbers 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

To find :

Median of 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

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 numbers

Here the given numbers are 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

Step 2 of 3 :

Rearrange in ascending order

Rearranging in ascending order we get

2, 5 , 7 , 7 , 8 , 8 , 10 , 10 , 14 , 15 , 17 , 18 , 24 , 27 , 28 , 48

Step 3 of 3 :

Find the median of the numbers

Number of observations = 16 which is even

Therefore the required median

= The middle terms of the whole arranged observations

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

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {\bigg( \frac{16 }{2} \bigg)}^{th} \: observation +{\bigg( \frac{16}{2} + 1 \bigg)}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {8}^{th} \: observation +{9}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times (10 + 14) }$

$\displaystyle \sf{ = \frac{1}{2} \times 24 }$

$\displaystyle \sf{ = 12 }$

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