Question

The points scored by the team of kabaddi in a series of matches are given below : Find the median of the points scored by the team. 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7,18, 28. *​

Answer 1

Given :-

The points scored by the team of kabaddi in a series of matches are given below :

$⇝ \:$ 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7,18, 28.

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To Find :-

• What is the median of the points score by the team ?

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Formula Used :-

♣ Median Formula :

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

Where,

• n = Number of Observations

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Solution :-

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

$⟼ \: \sf17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7,18, 28.$

$⟼ \: \bf 2, 5, 7, 7, 8, 8, 10, 10, 14, 15, 17, 18, 24, 27, 28, 48$

Now, We have to find the number of Observations :

$⟼ \: \sf 2, 5, 7, 7, 8, 8, 10, 10, 14, 15, 17, 18, 24, 27, 28, 48$

So,

$\bf⟶ \: \purple {Number \: Of \: Observations = 16}$

As we can observe there are 16 number of observations and 16 is an even number.

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

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

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

$⟹ \: \displaystyle \sf Median \: = \frac{ \: \displaystyle \sf8^{th}Observation \: + \: \bigg( 8 +1 \bigg)^{th}Observation }{2}$

$⟹ \: \displaystyle \sf Median \: = \frac{ \: \displaystyle \sf8^{th}Observation \: + \: 9^{th}Observation }{2}$

Now,

➳ 2 = 1st Observation

➳ 5 = 2nd Observation

➳ 7 = 3rd Observation

➳ 7 = 4th Observation

➳ 8 = 5th Observation

➳ 8 = 6th Observation

➳ 10 = 7th Observation

➳ 10 = 8th Observation

➳ 14 = 9th Observation

➳ 15 = 10th Observation

➳ 17 = 11th Observation

➳ 18 = 12th Observation

➳ 24 = 13th Observation

➳ 27 = 14th Observation

➳ 28 = 15th Observation

➳ 48 = 16th Observation

So, according to this term we get,

$⟹ \: \displaystyle \sf Median \: = \: \frac{ \sf10 \: + \: 14 }{2}$

$⟹ \: \displaystyle \sf Median \: = \: \cancel\frac{ \sf24 }{2}$

$⟹ \: \displaystyle \sf Median \: = \: \frac{ \sf12 }{1}$

$\displaystyle⟹ \red{\bf \: Median \: = \: 12}$

∴ The median is 12 .

Hence, the median of the points score by the team is 12 .

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☬ Note :-

That 12 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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