Question

Find the median of the following ungrouped data:

4, 2, 3, 4, 8, 5, 9

(a) 7 (b) 4.5 (c) 4 (d) 7.5
​

Answer 1

Answer:

Given :-

• The data is 4, 2, 3, 4, 8, 5, 9.

To Find :-

• What is the median.

Solution :-

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

$\longrightarrow \sf 4, 2, 3, 4, 8, 5, 9$

So, it will be :

$\longrightarrow \bf 2, 3, 4, 4, 5, 8, 9$

Hence,

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

As we know that :

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

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

where,

• n = Number of Observations

According to the question by using the formula we get,

$\implies \sf Median =\: \bigg(\dfrac{n + 1}{2}\bigg)^{th}\: term$

Here,

• n = Number of Observations = 7

$\implies \sf Median =\: \bigg(\dfrac{7 + 1}{2}\bigg)^{th}\: term$

$\implies \sf Median =\: \bigg(\dfrac{8}{2}\bigg)^{th}\: term$

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

Here,

➳ 2 = 1st term

➳ 3 = 2nd term

➳ 4 = 3rd term

➳ 4 = 4th term

➳ 5 = 5th term

➳ 8 = 6th term

➳ 9 = 7th term

Hence,

$\implies \sf\bold{\red{Median =\: 4}}$

$\therefore$ The median is 4 .

Hence, the correct options is option no (c) 4 .