Question

Use the box plot to answer the questions. What is the range of Charles’s scores? What is the median of Charles’s scores? What is the IQR of Charles’s scores?.

Answer 1

Box-plot describes 5 important data of the observations. We get following values for range, median and IQR as:

• The range of Charles' scores is 20
• The median of Charles' scores is 90
• The IQR of Charles' scores is 8

How does a boxplot shows the  data points?

A box plot has 5 data description.

• The leftmost whisker shows the minimum value in the data.
• The rightmost whisker shows the maximum value in the data.
• The leftmost line in the box shows the first quartile.
• The middle line shows the median, also called second quartile.
• The last line of the box shows the third quartile.

How to find the interquartile range?

IQR(inter quartile range)  is the dfference between third and first quartile. (Its the horizontal length of the box)

What is the range of a data set?

Range = Maximum value of the data set - Minimum value of the dataset

The missing box plot is attached below for the given problem.

From the given data, we see that, the left and right whiskers are on  80 and 100 respectively.

The left and right limit of the box are on 85 and 93 respectively.

The middle line lies on 90.

Thus, we get:

• Minimum score = left whisker = 80
• Maximum score = right whisker = 100
• First quartile = left limit of box = 85
• Third quartile = right limit of box = 93
• Second quartile = median = middle line's position in the box = 90

Thus, we get:

• Range of Charles' score = Max - min value = 100 = 80 = 20
• Median of Charles' score =  90
• IQR = third quartile - first quartile = 93 - 85 = 8

Learn more about box plot here:

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