Algebra 1 Name______Notes – 8.1

Measures of Central Tendency and Spread & Box-and-Whisker Plots

Opener – Find the average of the given set of data.

23 25 34 36 19 25 17 23 22 39 36

Measures of Central Tendency mean –

median –

mode –

Example 1: Find the measures of central tendencies given the set of data. The tuition costs (in thousands of dollars) for ten different liberal arts colleges are listed below.

38 33 40 27 44 32 23 27 47 31

Think About It! A – If the data value of “23” were changed to “26”, what would be the effect on the mean, median, and mode?

B – If the data value of “33” were changed to “32”, what would be the effect on the mean, median, and mode?

Practice 2: Find the measure of central tendencies given the set of data. The tuition costs (in thousands of dollars) for ten different liberal arts colleges are listed below.

43 33 31 40 31 27 42 47 32 41

The Five Number Summary min =

Q1 = med =

Q3 = max =

Measures of Spread range –

lower quartile range –

upper quartile range –

interquartile range (IQR) –

Example 3: Use the data given to find the following.

22 17 18 29 22 22 23 24 23 17 21

Minimum =

Q1 =

Median =

Q3 =

Maximum =

Range =

IQR = Box-and-Whisker Plot

Example 4: The last 11 credit card purchases (rounded to the nearest dollar) for someone are given.

22 66 44 91 12 45 48 31 20 82 19

Fill in each value and the create a box-and-whisker plot.

Min =

Q1 =

Median =

Q3 =

Max =

Analyzing and Comparing Box-and-Whisker Plots Examples 5 – 8: Examine the box plot. 5. What is the value of the third quartile?

6. What is the median score?

7. What percent of the values are less than 4?

8. What is the range of the data presented in the box plot?

Practice 9 – 11: The box plot shows the ages of people attending a music concert. 9. What is the IQR for the data?

10. What percentage of the ages are 15 and older?

11. What is the median age?

Examples 12 – 15: The box plot shows the lengths of cell phone calls made by three students in a one-week period. 12. Which student made the longest call?

13. Which student made the shortest call?

14. Which student had the largest IQR?

15. Which student had the smallest lower quartile range?

Practice 16 – 19: The box plot compares the annual incomes of three professions. 16. Which profession has the lowest income?

17. Which profession has the largest median income?

18. Which profession has the largest range in income?

19. Which profession has the smallest IQR?