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## Key Concepts

• Make a box plot.
• Make a box plot when the number of values is even.
• Interpret a box plot.

## Display data in box plots

### Introduction

In this chapter, we will learn to make a box plot, make a box plot for a data set whose number of values is even and interpret a box plot.

### Box plot

A box plot is a diagram that shows the distribution of data values using the median, quartiles, minimum values and maximum value on a number line.

### Quartiles

Quartiles are values that divide a data set into four equal parts.

A data plot visually represents a data set divided into four equal parts or quartiles.

### Steps to draw a dot plot

• Find the median of all of the data.
• Find Q1, which is the median of the first quartile, and Q3, which is the median of the second quartile of the data.
• Draw a number line, and then draw a box from Q1 to Q3 points.
• Draw a vertical line in the box at the value of the median.
• Draw a line segment connecting the minimum value to the box and a line segment that connects the maximum value to the box.

You will end up with a graph that looks like this:

### Make a box plot

Example 1:

Eric’s scores on the test were given below,

79, 75, 91, 73, 83, 77, 81, 89, 87, 85, and 79.

Draw a box plot that shows the distribution of Eric’s test scores.

Solution:

Step 1:

Order the values from least to greatest,

73, 75, 77, 79, 79, 81, 83, 85, 87, 89, 91

Step 2:

Find the minimum, median, and maximum values of the data.

Step 3:

Find the median for each half.

Step 4:

Draw the box plot on a number line, a box between the first and third quartiles, and a vertical segment that shows the median. The test scores range from 73 to 91 in 2 increments. So, a good scale for the number line is 73 to 91, numbered by 2s.

### Make a box plot when the number of values is even

Example 2:

Sarah went to a nearby lake for fishing. The lengths in inches of the fishes caught by Sarah are given below.

7, 8, 8, 12, 13, 14, 16, 16, 18, 22, 23, 25

Draw a box plot that shows the distribution of lengths of fishes.

Solution:

Step 1:

Find the minimum, median, and maximum values as well as the first and third quartiles.

Draw the box plot on a number line with an approximate scale, a box between the first and third quartiles, and a vertical segment that shows the median.

### Interpret a box plot

Example 3:

The box plot shows the speeds of keyboarding, in minutes, of words typed. What information do you know from the box plot?

Solution:

The minimum is 20, so the slowest keyboarder can type 20 words per minute.

The maximum is 90, so the fastest keyboarder can type 90 words per minute.

The median speed of the keyboarding is about 70 words per minute.

The first quartile speed is 40 words, and the third quartile speed is 80 words.

## Exercise

• Fill in the blanks:

A box plot shows the distribution of data values using the _______________, _________________, ______________________, and _____________ on a number line.

• The lengths of the 11 fishes caught by Robin are given below.
7, 9, 12, 12, 13, 14, 15, 16, 18, 22, 23
How is the distribution of Robin’s data? Draw a box plot.
• The ages of 12 employees working in a company are listed below.
16, 28, 10, 16, 22, 10, 22, 10, 16, 22, 22, 25
Record their ages in a box plot.
• Mike’s scores on tests were 79, 75, 82, 90, 73, 82, 77, 85, and 77.
a.  What are the minimum and maximum test scores scored by Mike?
b.  Find the median of test scores.
c.  Find the first and the third quartiles.
d.  Draw a box plot that shows the distribution of Mike’s test scores.
• The data set shows how many minutes Jack practiced the guitar each day for 10 days. 40, 25, 45, 55, 30, 25, 30, 50, 30, 40

Find the statistical measures that you need to make a box plot of Jack’s practice times of guitar.

• The following data set shows the prices, in dollars, of tickets to 10 plays at a movie theater. 15, 23, 9, 15, 17, 9, 21, 15, 11, 19 Find the minimum, median, maximum, first quartile and third quartile.
• Make a box plot for the scores scored on math tests, 74, 79, 67, 62, 86, 91, 100, 77, 65, 71, 73, 73, 94, 82.
• The maximum speeds of certain kinds of fish are summarized in the below box plot. What information do you know from the box plot?
• The box plot below summarizes data from a survey of households about the number of mobiles they have. What information do you know from the box plot?
• The scores of a certain class on a test about real numbers are summarized in the box plots below. What information do you know from the box plot?

### What have we learned

• Make a box plot to show the representation of data values of a data set.
• Make a data plot for a data set whose number of values is even.
• Interpret a box plot and analyse minimum, maximum and mode values.

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