NOTES & Practice: Box & Whisker Plots Name

What is Statistics?

My Thoughts Class Thoughts

Box and Whiskers Plot

A box-and-whisker plot is a diagram that divides data into ____ equal parts(25%). To do this,

first find the ___________ of the data, and then find the ____________ of the lower half, called

the ___________ quartile, and the median of the upper half, called the __________ quartile.

Median of an even number of data points: 76, 80, 91, 75, 76, 100

Median of an odd number of data points: 2.1, 3.0, 4.5, 4.9, 2.5

What is an outlier?

Example 1: Data Set: Math test scores {80, 75, 90, 95, 65, 65, 80, 85, 70, 100}

Reorder the data from least to greatest.

Find the median, lower quartile (LQ), upper quartile (UQ), lower extreme, and upper extreme.

Plot these points on a number line:

Draw a box around the lower and upper quartiles. Draw a line through the median point. Draw the whiskers from each end of the box to the lower and upper extremes.

Example 2:

12, 23, 6, 17, 9, 10, 19, 7, 11, 15, 7, 12, 13, 20

1. Reorder the numbers from _________ to ____________!

2. Find the median of the set of numbers:

3. Find the median of the _________ half:

4. Find the median of the _________ half:

5. Create a number line.

6. Put a dot over the lower extreme (the ______________).

7. Put a dot over the upper extreme (the ______________).

8. Put a dot over the median, the lower quartile and the upper quartile.

9. Draw the box and whiskers.

GUIDED PRACTICE

1. Make a box-and-whisker plot for the set of data.

15, 16, 7, 8, 5, 5, 3, 4, 8

a. Reorder the numbers b. Find the median of all the numbers c. Find the lower and upper quartile

d. What are the lower and upper extremes?

2. Use the chart at right.

a. Order the data:

b. What are the lower and upper extremes?

c. What is the median?

d. What are the lower and upper quartiles?

e. What is the range?

3. Refer to the table at the right. It shows the regular season games lost by each National League baseball team in a year.

a. Reorder the data.

b. Find the lower extreme, LQ, median, UQ, and upper extreme.

c. Draw a box-and-whisker plot of the data.

d. What fraction of the data is between 73 and 78?

e. Between what two numbers is the largest range of the four quartiles?

f. Find the interquartile range.

g. Are there any outliers? If so, identify them.

4. Interpret the box and whisker plots. a. Using the box and whisker plot

shown, in which year was the corn yield more varied? Explain.

b. How does the median yield in 2009 compare with the median yield in 2007?

c. What was the range of corn yield in 2009?

d. What was the interquartile range in 2007?

e. Between what two numbers is the largest range of the four quartiles in 2009?

Try It!

5. Make a box and whisker plot for the following set of data.

{$105, $98, $83, $127, $115, $114, $132, $93, $107, $101, $119}

a. Order the data:

b. What are the lower and upper extremes?

c. What is the median?

d. What are the lower and upper quartiles?

e. What is the range?

2007

2009