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 shown below.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
You can also visit the following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Analytical geometry calculators
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Ratio and proportion shortcuts
Converting repeating decimals in to fractions