Question

the median in the set 6,4,2,3,4,5,5,4 would be​

Answer 1

Answer:

Hey mate this is your answer

Answer 2

Median of the numbers 6 , 4 , 2 , 3 , 4 , 5 , 5 , 4 is 4

Given :

The numbers 6 , 4 , 2 , 3 , 4 , 5 , 5 , 4

To find :

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

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 6 , 4 , 2 , 3 , 4 , 5 , 5 , 4

Step 2 of 3 :

Rearrange in ascending order

Rearranging in ascending order we get

2 , 3 , 4 , 4 , 4 , 5 , 5 , 6

Step 3 of 3 :

Find the median of the numbers

Number of observations = 8 which is even

Therefore the required median

= The middle terms of the whole arranged observations

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

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

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {4}^{th} \: observation +{5}^{th} \: observation \bigg] }$

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

$\displaystyle \sf{ = \frac{1}{2} \times 8 }$

$\displaystyle \sf{ = 4 }$

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