1. Bellwork
1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92.
2. Find the median of the test scores.
79, 87, 88, 89, 91, 92, 93 89

2. Box-and-Whisker Plots
Section 11.2

3. Step 1 – Order Numbers
Step 1. Order the set of numbers from least to greatest

4. Step 2 – Find the Median
Step 2. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median?

5. Step 3 – Upper & Lower Quartiles
Step 3: Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they?

6. Step 4 – Draw a Number Line
Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data:

7. Step 5 – Draw the Parts
Step 4: Locate the main median 12 using a vertical line just above your number line:

8. Step 5 – Draw the Parts
Locate the lower median 8.5 and the upper median 14 with similar vertical lines:

9. Step 5 – Draw the Parts
Next, draw a box using the lower and upper median lines as endpoints:

10. Step 5 – Draw the Parts
Finally, the whiskers extend out to the data's smallest number 5 and largest number 20:

11. Step 6 - Label the Parts of a Box-and-Whisker Plot
Lower Quartile
Median
Upper Quartile
Lower Extreme 3 1 2
Upper Extreme 4 5
Name the parts of a Box-and-Whisker Plot

12. The lower fourth and upper fourth quarters are represented by “whiskers” that extend to the minimum (least) and maximum (greatest) values.
Data set: 85,92,78,88,90,88,89
Median
Upper quartile
Lower quartile
What are minimum and maximum values?

13. Litter Size 2 3 4 5 6 Number of Litters 1 8 11
The table below summarizes a cat breeder’s records for kitten litters born in a given year. You can divide the data into four equal part using quartiles.
Litter Size 2 3 4 5 6
Number of Litters 1 8 11

14. You know that the median of a data set divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
Lower quartile: 3 median of lower half
Median: 4
Upper quartile: 5 median of upper half

15. You know that the median of a data set divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile.
Kitten Data
Lower half
Upper half
Lower quartile: 3 median of lower half
Median: 4
Upper quartile: 5 median of upper half

16. c What letter is the _____? F E D Lower half Upper half B A B c
How do you know?

17. *It helps you to interpret and represent data.
Importance
Why do we need to know how to display and analyze data in box-and-whisker plots ?
*It helps you to interpret and represent data.
*It gives a visual representation of data.
Tell your partner which reason is most important to you. You can use one of mine or one of your own.
p/s - volunteers

18. Bellwork Make a box-and-whisker plot that represents the data.
Cat lengths (in inches): 16, 18, 20, 25, 17, 22, 23, 21
Bellwork

19. Find the lower and upper quartiles for the data set.
Order the data from least to greatest.
Find the median.
Find the median of the lower half – lower quartile
Find the median of the upper half – upper quartile
I do
A. 15, 83, 75, 12, 19, 74, 21
Order the values.
lower quartile: 15
upper quartile: 75
How did I find the lower and upper quartiles?

20. Find the lower and upper quartiles for the data set.
Order the data from least to greatest.
Find the median.
Find the median of the lower half – lower quartile
Find the median of the upper half – upper quartile
We do
B. 75, 61, 88, 79, 79, 99, 63, 77
Order the values.
lower quartile: = 69 2
upper quartile: = 83.5 2

21. Find the lower and upper quartiles for the data set.
Order the data from least to greatest.
Find the median.
Find the median of the lower half – lower quartile
Find the median of the upper half – upper quartile
We do
A. 25, 38, 66, 19, 91, 47, 13
Order the values.
lower quartile: 19
upper quartile: 66

22. Find the lower and upper quartiles for the data set.
Order the data from least to greatest.
Find the median.
Find the median of the lower half – lower quartile
Find the median of the upper half – upper quartile
You do
B. 45, 31, 59, 49, 49, 69, 33, 47
Order the values.
lower quartile: = 39 2
upper quartile: = 54 2

23. Use the given data to make a box-and-whisker plot.
Additional Example 2: Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker plot.
21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum.
minimum: 13
maximum: 25
lower quartile: = 16 2
upper quartile: = 21 2
median: = 19 2

24. Use the given data to make a box-and-whisker plot.
I do (cont.)
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above each value from Step 1.

25. Use the given data to make a box-and-whisker plot.
I do (cont.)
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.

26. Use the given data to make a box-and-whisker plot.
We do
Check It Out! Example 2
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum.
minimum: 23
maximum: 35
lower quartile: = 25 2
upper quartile: = 32 2
median: = 30 2

27. Use the given data to make a box-and-whisker plot.
We do (cont.)
Check It Out! Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above each value.

28. Use the given data to make a box-and-whisker plot.
We do (cont.)
Check It Out! Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
Step 2. Draw a number line and plot a point above each value.

29. Step 1. Order the data from least to greatest
Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum.
Step 2. Draw a number line and plot a point above each value.
Step 3. Draw the box and whiskers.

30. The box-and-whisker plot represents the lengths (in seconds) of the songs played by a rock band at a concert.
Find and interpret the range of the data.
b. Describe the distribution of the data.
c. Find and interpret the interquartile range of the data.
d. Are the data more spread out below Q1 or above Q3? Explain.

37. Describing the Shape of a Distribution
Step 1 Draw and label the axes.
Describing the Shape of a Distribution
Step 2 Draw a bar to represent the frequency of each interval. The data on the right of the distribution are approximately a mirror image of the data on the left of the distribution.
So, the distribution is symmetric.

38. Choosing Appropriate Measures
Step 1: Make a frequency table using the described
intervals. Then use the frequency table to make a
histogram.
Choosing Appropriate Measures
Step2: Because most of the data are on the right and the tail of
the graph extends to the left, the distribution is skewed left. So,
use the median to describe the center and the five-number
summary to describe the variation.
Step3: Using the frequency table and the histogram, you can see
that most of the speeds are more than 45 miles per hour. So, most
of the motorists were speeding.

39. Comparing Data Distributions
Because the data on the right of the distribution for the female
students are approximately a mirror image of the data on the left
of the distribution, the distribution is symmetric. So, the mean
and standard deviation best represent the distribution for female
students.
Comparing Data Distributions
Because most of the data are on the left of the distribution for
the male students and the tail of the graph extends to the right,
the distribution is skewed right. So, the median and five-number
summary best represent the distribution for male students.
The mean of the female data set is probably in the 30–39 interval, while the median of the male data set is in the 10–19 interval. So, a typical female student is much more likely to use emoticons than a typical male student.
The data for the female students is more variable than the data for the male students. This means that the use of emoticons tends to differ more from one female student to the next.

40. Compare the distributions using their shapes and appropriate measures of center and variation.

41. Comparing Data Distributions
The table shows the results of a survey that asked men and women
how many pairs of shoes they own.
Comparing Data Distributions
Make a double box-and-whisker plot that represents the data. Describe the shape of each distribution.
b. Compare the number of pairs of shoes owned by men to the number of pairs of shoes owned by women.
c. About how many of the women surveyed would you expect to own between 10 and 18 pairs of shoes?
The distribution for men is skewed right, and
the distribution for women is symmetric.

43. Solve for x
the mean is 6.
The median is 18
Bellwork