**Box and whisker plot :**

Box and whisker-plot is the graph used in statistics to represent the central 50% of the values of a data set.

The picture figure given below clearly illustrates this.

In the above figure, the box spans interquartile range (central 50%).

To draw box and whisker-plot graph for a data set, we have to know lower quartile, upper quartile and median.

To construct box and whisker-plot for the given data set, we have to do the following steps.

Step 1 :

Write the observations of the given data set in ascending order.

Step 2 :

Find lower quartile, upper quartile and median using the formulas given below.

Lower quartile = (n+1)/4

Upper quartile = 3(n+1)/4

Median = (n+1)/2

Here, n = number of observations in the given data set.

Step 3 :

Using lower quartile, upper quartile and median, we have to construct box and whisker-plot as given in the above picture.

Construct box and whisker-plot for the data given below.

4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4

**Construction of box and whisker-plot :**

**Step 1 : **

Let us write the observations in the data in ascending order.

3.9, 4.1, 4.2, 4.3, 4.3, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1

**Step 2 : **

Number of observations (n) = 17

Let us find lower quartile, upper quartile and median.

**Lower quartile : **

Lower quartile = (n+1)/4 = (17+1)/4 = 18/4 = 4.5

Lower quartile comes in between 4th and 5th observations.

So, lower quartile = average of 4th and 5th observations

Lower quartile = (4.3 + 4.3)/2 = 8.6/2 = 4.3

**Upper quartile : **

Upper quartile = 3(n+1)/4 = 3(17+1)/4 = 54/4 = 13.5

Upper quartile comes in between 13th and 14th observations.

So, upper quartile = average of 13th and 14th observations

Upper quartile = (4.7 + 4.8)/2 = 9.5/2 = 4.75

**Median : **

Median = (n+1)/2 = (17+1)/2 = 18/2 = 9

Median is exactly the 9th observation.

So, median = 4.4

**Step 3 : **

Using lower quartile, upper quartile and median, we can construct box and whisker-plot graph as given below.

After having gone through the stuff given above, we hope that the students would have understood "Box and whisker-plot".

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