Question

find the median 1,2,3,4,5,6​

Answer 1

Answer:

Step-by-step explanation:

Median of 1, 2, 3, 4, 5, 6

∵ total no. is even

median = {(n/2)th term + (n/2+1)th term} / 2

             = (3rd term + 4th term)/2

             = (3 + 4)/2

             = 7/2

 Median= 3.5

Answer 2

Median of 1 , 2 , 3 , 4 , 5 , 6 is 3.5

Given :

The observations 1 , 2 , 3 , 4 , 5 , 6

To find :

Median of 1 , 2 , 3 , 4 , 5 , 6

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 2 :

Write down the given observations

Here the given observations are 1 , 2 , 3 , 4 , 5 , 6

Step 2 of 2 :

Find the median of the scores

Number of observations = 6 which is even

Therefore the required median

= The middle terms of the whole arranged observations

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

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

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

$\displaystyle \sf{ = \frac{1}{2} \times (3 + 4) }$

$\displaystyle \sf{ = \frac{1}{2} \times 7 }$

$\displaystyle \sf{ = 3.5 }$

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