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# Box and Whisker Plot Calculator

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Box and Whisker plot represents data to show the minimum, maximum, median, first and third quartile range of the given set. This online Box and Whisker Plot Calculator will find the first three quartiles of the given data. The first and second quartile equation is given below. The median is the second quartile.

First quartile ($Q_1$) = $\frac{(n+1)}{4}$

Third quartile ($Q_3$) = $\frac{3(n+1)}{4}$
where, n is the total number of observations.

## Steps

Step 1 : Write the given observation in ascending order.

Step 2 :
The middle value in the given observation is the median i.e. second quartile ($Q_3$). If there are two middle values of the data, the average of both the values gives you the median value.

Step 3 :
Use the above formula to find the first quartile($Q_1$) and the third quartile ($Q_3$).

## Problems

Below are the problems based on Box and Whisker Plot Calculator.

### Solved Examples

Question 1:
Find the three quartiles of the below data .
80, 75, 90, 95, 65, 65, 80, 85, 70, 100

Solution:
Step 1 : Ascending order of the given observation is
65, 65, 70, 75, 80, 80, 85, 90, 95, 100

Step 2 :
The median of the given observation is given by,
Median $Q_2$ = 80

Step 3 :
First quartile $Q_1$, = $\frac{(n+1)}{4}$

= $\frac{(10+1)}{4}$

= 2.75

Third quartile $Q_3$, = $\frac{3(n+1)}{4}$

= $\frac{3(10+1)}{4}$

= 8.25

Answer  : First three quartiles are, $Q_1$ = 2.75, $Q_2$ = 80, $Q_3$ = 8.25.

Question 2: Find the three quartiles of the below data.
9, 33, 27, 4, 15, 35, 7, 31, 20, 23, 6, 18
Solution:

Step 1 : Ascending order of the given observation is
4, 6, 7, 9, 15, 18, 20, 23, 27, 31, 33, 35

Step 2 :
The middle values of the given data are 18 and 20. Therefore, the median of the given observation is given by,
Median $Q_2$ = $\frac{(18+20)}{2}$ = 19

Step 3 :
First quartile $Q_1$, = $\frac{(n+1)}{4}$

= $\frac{(12+1)}{4}$

= 3.25

Third quartile $Q_3$, = $\frac{3(n+1)}{4}$

= $\frac{3(12+1)}{4}$

= 8.25

Answer  : First three quartiles are, $Q_1$ = 3.25, $Q_2$ = 19, $Q_3$ = 8.25.