Question

4. Find the median of 5, 7, 10,9,5, 12, 15, 12, 18, 20. If 9 is replaced by 14, what will be the new mediab​

Answer 1

Answer:

(i) median is 11

(ii) median is 12

Step-by-step explanation:

first we have to arrange this data in

ascending order :

5,5,7,9,10,12,12,15,18,20

if n is even then ,

$median = \frac{ \frac{n}{2}th \: observation \: + ( \frac{n + 1}{2})th \: observation }{2}$

So here n = 10

$median \: = \frac{ \frac{10}{2}th \: observtion \: +( \frac{10}{2} + 1)th \: observtion \: }{2}$

$median = \frac{5th \: observtion \: + 6th \: observation}{2}$

$median = \frac{10 + 12}{2}$

$median = \frac{22}{2}$

$median = 11$

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Now if we replace 9 by 14 new data is

5,5,7,10,12,12,14,15,18,20

$median = \frac{5th \: observation \: + 6th \: observation}{2}$

$median \: = \frac{12 + 12}{2}$

$median = \frac{24}{2}$

$median = 12$

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Answer 2

Answer:

median is 11 and when 9 is replaced by 14 then new median is 12