Given that set A is ( 3, 7, 8, 5, 14, 14, 21, 15, 18, 14) and we need to find What is the First quartile and 3rd quartile?

To solve this lets arrange the set in ascending order. We get

3, 5, 7, 8, 14, 14, 14, 15, 18, 21 => 10 numbers

Median of the set will be the mean of middle two terms = \(\frac{14 + 14}{ 2}\) = 14

(Watch this Video to know more about Medians and Statistics)

Now, the Median divides the set into two parts
First half -> 3, 5, 7, 8, 14
Second Half -> 14, 14, 15, 18, 21

First Quartile or \(Q_1\) is the Median of the first half = Middle value = 7
Third Quartile or \(Q_3\) is the Median of the second half = Middle value = 15

So, Answer will be 7 and 15.
Hope it helps!

Asmakan: In case of odd number of values we keep the middle value as the Median or \(Q_2\) and Ignore the Median value while dividing the set into first and second half.

Ex: If the set is as follows:
1, 2, 3, 4, 5, 6, 7
Then \(Q_2\) or Median = 4
First Half = 1, 2, 3 => \(Q_1\) = 2
Second Half = 5, 6, 7 => \(Q_3\) = 6

Watch the following video to learn the Basics of Box and Whisker Plot