Question

the median of the data 1,2,9,8,7,6 and 10 is​

Answer 1

Answer:

Given :-

• The data is 1 , 2 , 9 , 8 , 7 , 6 and 10.

To Find :-

• What is the median.

Solution :-

First, we have to arrange the data into ascending order :

$\longrightarrow \sf 1 , 2 , 9 , 8 , 7 , 6 , 10$

So, it will be :

$\longrightarrow \bf 1 , 2 , 6 , 7 , 8 , 9 , 10$

Hence,

$\mapsto \sf\bold{\blue{Number\: of\: Observations =\: n = 7(Odd)}}$

As we know that :

$\clubsuit$ Median formula when the number of observation is odd :

$\bigstar \: \: \sf\boxed{\bold{\pink{Median =\: \bigg\lgroup \dfrac{n + 1}{2}\bigg\rgroup ^{th}\: term}}}\: \: \: \bigstar$

where,

• n = Number of Observation

According to the question by using the formula we get,

$\dashrightarrow \bf Median =\: \bigg\lgroup \dfrac{n + 1}{2}\bigg\rgroup ^{th}\: term$

Here,

• n = Number of observation = 7

$\dashrightarrow \sf Median =\: \bigg\lgroup \dfrac{7 + 1}{2}\bigg\rgroup ^{th}\: term$

$\dashrightarrow \sf Median =\: \bigg\lgroup \dfrac{\cancel{8}}{\cancel{2}}\bigg\rgroup ^{th}\: term$

$\dashrightarrow \sf Median =\: 4^{th}\: term$

Here,

➳ 1 = 1st term

➳ 2 = 2nd term

➳ 6 = 3rd term

➳ 7 = 4th term

➳ 8 = 5th term

➳ 9 = 6th term

➳ 10 = 7th term

Hence,

$\dashrightarrow \sf\bold{\red{Median =\: 7}}$

$\therefore$ The median is 7 .

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EXTRA INFORMATION :-

$\clubsuit$ Median formula when the number of observation is even :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Median =\: \dfrac{\bigg\lgroup \dfrac{n}{2}\bigg\rgroup ^{th}\: term\: + \bigg\lgroup \dfrac{n}{2} + 1\bigg\rgroup ^{th}\: term}{2}}}}\: \: \bigstar$

where,

• n = Number of Observations

$\clubsuit$ Mean Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: Of\: Observations}{Total\: Numbers\: Of\: Observations}}}}\: \: \: \bigstar$