# BOX PLOT WORKSHEET

Problem 1 :

Make a box-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

Problem 2 :

The heights of several students are shown.

Make a box-plot for the data.

Problem 1 :

Make a box-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

Solution :

Making box 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 make box-plot graph as given below.

Problem 2 :

The heights of several students are shown.

Make a box-plot for the data.

Solution :

Making box-plot :

Step 1 :

Order the data and find the needed values.

Step 2 :

Draw the box-plot.

Draw a number line that includes all the data values.

On the number line, draw dots above the least value, the lower quartile, the median, the upper quartile, and the greatest value.

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