Question

find the median of the following data : 4,1,2,3,1,2,2,3,5,7​

Answer 1

Answer:

(n/2+n+1/2)/2 = median.

(10/2+10+1/2)/2= 5.5

hope it helps you.

Answer 2

Given :-

$⇝ \:$ 4,1,2,3,1,2,2,3,5,7

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To Find :-

• What is the median of the following data ?

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Formula Used :-

♣ Median Formula :

$\bigstar \: \: \displaystyle \boxed{ \bf \pink{Median \: = \frac{ \bigg( \displaystyle \bf\frac{n}{2} \bigg) ^{th}Observation \: + \: \bigg( \frac{n}{2} +1 \bigg)^{th}Observation }{2} }} \: \bigstar$

Where,

• n = Number of Observations

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Solution :-

First, We have to arrange all the observations in ascending order :

$⟼ \: \sf 4, 1, 2, 3, 1, 2, 2, 3, 5, 7$

$⟼ \: \bf 1, 1, 2, 2, 2, 3, 3, 4, 5, 7$

Now, We have to find the number of Observations :

$⟼ \: \sf 1, 1, 2, 2, 2, 3, 3, 4, 5, 7$

So,

$\bf⟶ \: \purple {Number \: Of \: Observations = 10}$

As we can observe there are 10 number of observations and 10 is an even number.

So, according to the question by using formula we get,

$⟹ \: \displaystyle \bf Median \: = \frac{ \bigg( \displaystyle \bf\frac{n}{2} \bigg) ^{th}Observation \: + \: \bigg( \frac{n}{2} +1 \bigg)^{th}Observation }{2}$

$⟹ \: \displaystyle \sf Median \: = \frac{ \bigg( \displaystyle \sf\frac{n}{2} \bigg) ^{th}Observation \: + \: \bigg( \frac{n}{2} +1 \bigg)^{th}Observation }{2}$

$⟹ \: \displaystyle \sf Median \: = \frac{ \: \displaystyle \sf5^{th}Observation \: + \: \bigg( 5 +1 \bigg)^{th}Observation }{2}$

$⟹ \: \displaystyle \sf Median \: = \frac{ \: \displaystyle \sf5^{th}Observation \: + \: 6^{th}Observation }{2}$

Now,

➳ 1 = 1st Observation

➳ 1 = 2nd Observation

➳ 2 = 3rd Observation

➳ 2 = 4th Observation

➳ 2 = 5th Observation

➳ 3 = 6th Observation

➳ 3 = 7th Observation

➳ 4 = 8th Observation

➳ 5 = 9th Observation

➳ 7 = 10th Observation

So, according to this term we get,

$⟹ \: \displaystyle \sf Median \: = \: \frac{ \sf 2 \: + \: 3 }{2}$

$⟹ \: \displaystyle \sf Median \: = \: \cancel\frac{ \sf 5 }{2}$

$⟹ \: \displaystyle \sf Median \: = \: \frac{ \sf \: 2.5 }{1}$

$\displaystyle⟹ \red{\bf \: Median \: = \: 2.5}$

∴ The median is 2.5 .

Hence, the median of the given data is 2.5 .

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☬ Note :-

That 2.5 was not in the list of numbers... but that is OK because half the numbers in the list are less, and half the numbers are greater.

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