Unit 8, Lesson 16
Box Plots
Grade 6
16.3
Activity
Twenty people participate in a study about blinking. The number of times each person blinked while watching a video for one minute is recorded. The data values are shown here, in order from smallest to largest.
- 3
- 6
- 8
- 11
- 11
- 13
- 14
- 14
- 14
- 14
- 16
- 18
- 20
- 20
- 20
- 22
- 24
- 32
- 36
- 51
- Here is a dot plot showing these data.
- Find the median (Q2) and mark its location on the dot plot.
- Find the first quartile (Q1) and the third quartile (Q3). Mark their locations on the dot plot.
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What are the minimum and maximum values?
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A box plot can be used to represent the five-number summary graphically. Let’s draw a box plot for the number-of-blinks data. Above the dot plot:
- Draw a box that extends from the first quartile (Q1) to the third quartile (Q3). Label the quartiles.
- At the median (Q2), draw a vertical line from the top of the box to the bottom of the box. Label the median.
- From the left side of the box (Q1), draw a horizontal line (a whisker) that extends to the minimum of the data set. On the right side of the box (Q3), draw a similar line that extends to the maximum of the data set.
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Compare the information that can be quickly understood from each representation.
Student Lesson Summary
A box plot represents the five-number summary of a data set.
It shows the first quartile (Q1) and the third quartile (Q3) as the left and right sides of a rectangle, or a box. The median (Q2) is shown as a vertical segment inside the box. On the left side, a horizontal line segment, sometimes called a whisker, extends from Q1 to the minimum value. On the right, a whisker extends from Q3 to the maximum value.
The rectangle in the middle represents the middle half of the data. Its width is the IQR. The whiskers represent the bottom quarter and the top quarter of the data set.
Here are data about pug and beagle weights represented as both dot plots and box plots.
Box plots and dot plots for two sets of data: "pug weights in kilograms” and "beagle weights in kilograms". The numbers 6 through 11 are indicated and there are tick marks midway between each indicated number. Each box plot is above it's corresponding dot plot. The approximate data for the box plot for "pug weights in kilograms" are as follows: Minimum value, 6. Maximum value, 8. Q1, 6.5. Q2, 7. Q3, 7.3. The approximate data for the dot plot for "pug weights in kilograms" are as follows: 6 kilograms, 1 dot. 6.2 kilograms, 2 dots. 6.4 kilograms, 2 dots. 6.6 kilograms, 2 dots. 6.8 kilograms, 2 dots. 7 kilograms, 3 dots. 7.2 kilograms, 3 dots. 7.4 kilograms, 1 dot. 7.6 kilograms, 2 dots. 7.8 kilograms, 1 dot. 8 kilograms, 1 dot. The approximate data for the box plot for "beagle weights in kilograms" are as follows: Minimum value, 9. Maximum value, 11. Q1, 9.6. Q2, 10. Q3, 10.5. The approximate data for the dot plot for "beagle weights in kilograms" are as follows: 9 kilograms, 1 x. 9.2 kilograms, 2 x's. 9.4 kilograms, 1 x. 9.6 kilograms, 3 x's. 9.8 kilograms, 1 x. 10 kilograms, 3 x's. 10.2 kilograms, 3 x's. 10.4 kilograms, 1 x. 10.6 kilograms, 2 x's. 10.8 kilograms, 2 x's. 11 kilograms, 1 x.
We can tell from the box plots that, in general, the pugs in the group are lighter than the beagles. The median weight of pugs is 7 kilograms and the median weight of beagles is 10 kilograms. Because the two box plots are on the same scale and the rectangles have similar widths, we can also tell that the IQRs for the two breeds are very similar. This suggests that the variability in the beagle weights is very similar to the variability in the pug weights.
A box plot is a way to represent data on a number line with a box and some lines. The data is divided into four sections by 5 values. Those values are the minimum, first quartile, median, third quartile, and maximum.