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 = (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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