Question

1
The median of the observations 8, 12, 7, 14, 6, 13, 15 will be -​

Answer 1

Answer:

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Step-by-step explanation:

arranging data in ascending order

6 < 7 < 8 < 12 < 13 < 14 < 15

after removing 1-1 term from first and last simultaneously, we get 12 as median

Answer 2

The median of the observations 8, 12, 7, 14, 6, 13, 15 will be 12

Given :

The observations 8, 12, 7, 14, 6, 13, 15

To find :

The median of the observations 8, 12, 7, 14, 6, 13, 15

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 observations

Here the given observations are 8, 12, 7, 14, 6, 13, 15

Step 2 of 3 :

Rearrange in ascending order

Rearranging in ascending order we get

6 , 7 , 8 , 12 , 13 , 14 , 15

Step 3 of 3 :

Find the median

Number of observations = 7 which is odd

Therefore the required median

= The middle terms of the whole arranged observations

$\displaystyle \sf{ = \frac{7 + 1}{2} \: th \: observation }$

$\displaystyle \sf{ = \frac{8}{2} \: th \: observation }$

$\displaystyle \sf{ = 4\: th \: observation }$

= 12

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