1. Measures of Dispersion
7-6 Statistics
Measures of Dispersion

2. WHAT YOU WILL LEARN
• To determine the following measure of dispersion:
Range
Standard deviation

3. Measures of Dispersion
Measures of dispersion are used to indicate the spread of the data.
The range is the difference between the highest and lowest values; it indicates the total spread of the data.
Range = highest value – lowest value

4. Example: Range
Nine different employees were selected and the amount of their salary was recorded. Find the range of the salaries.
$24,000 $32, $26,500
$56, $48, $27,000
$28, $34, $56,750
Range = $56,750  $24,000 = $32,750

5. Standard Deviation
The standard deviation measures how much the data differ from the mean. It is symbolized with s when it is calculated for a sample, and with  (Greek letter sigma) when it is calculated for a population.

6. To Find the Standard Deviation of a Set of Data
1. Find the mean of the set of data.
2. Make a chart having three columns:
Data Data  Mean (Data  Mean)2
3. List the data vertically under the column marked Data.
4. Subtract the mean from each piece of data and place the difference in the Data  Mean column.

7. To Find the Standard Deviation of a Set of Data (continued)
5. Square the values obtained in the Data  Mean column and record these values in the (Data  Mean)2 column.
6. Determine the sum of the values in the (Data  Mean)2 column.
7. Divide the sum obtained in step 6 by n  1, where n is the number of pieces of data.
8. Determine the square root of the number obtained in step 7. This number is the standard deviation of the set of data.

8. Example
Find the standard deviation of the following prices of selected washing machines:
$280, $217, $665, $684, $939, $299
Find the mean.

9. Example (continued), mean = 514
421,516
180,625
425
939
28,900
170
684
22,801
151
665
46,225
215
299
54,756
234
280
(297)2 = 88,209
297
217
(Data  Mean)2
Data  Mean
Data

10. Example (continued), mean = 514
The standard deviation is $

11. Or…. Press: “STAT” 1:Edit
Under L1, enter each item, pressing “Enter” after each entry
“List”
“MATH”
7:stdDev
2ND L1, then “ENTER”

12. Try This Example Again
Find the standard deviation of the following prices of selected washing machines:
$280, $217, $665, $684, $939, $299

13. Use the following data on the number of points scored in the Bay High School basketball games. What is the most common score?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 68 b. 70 c. 72 d. 75

14. Use the following data on the number of points scored in the Bay High School basketball games. What is the most common score?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 68 b. 70 c. 72 d. 75

15. Use the following data on the number of points scored in the Bay High School basketball games. What score do half of the games exceed?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 68 b. 70 c. 72 d. 75

16. Use the following data on the number of points scored in the Bay High School basketball games. What score do half of the games exceed?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 68 b. 70 c. 72 d. 75

17. Use the following data on the number of points scored in the Bay High School basketball games. About what percent of games have less than 75 points scored?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 25% b. 50% c. 75% d. 92%

18. Use the following data on the number of points scored in the Bay High School basketball games. About what percent of games have less than 75 points scored?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 25% b. 50% c. 75% d. 92%

19. Use the following data on the number of points scored in the Bay High School basketball games. About what percent of games have more than 88 points scored?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 92% b. 75% c. 50% d. 8%

20. Use the following data on the number of points scored in the Bay High School basketball games. About what percent of games have more than 88 points scored?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 92% b. 75% c. 50% d. 8%

21. Use the following data on the number of points scored in the Bay High School basketball games. If there are 20 games played throughout the season, what would be the total of all the points scored?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a b c d

22. Use the following data on the number of points scored in the Bay High School basketball games. If there are 20 games played throughout the season, what would be the total of all the points scored?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a b c d

23. Use the following data on the number of points scored in the Bay High School basketball games. What score represents 1.5 standard deviations above the mean?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 83 b c d

24. Use the following data on the number of points scored in the Bay High School basketball games. What score represents 1.5 standard deviations above the mean?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 83 b c d

25. Use the following data on the number of points scored in the Bay High School basketball games. What score represents 1 standard deviation below the mean?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 61 b. 59 c. 57 d. 50

26. Use the following data on the number of points scored in the Bay High School basketball games. What score represents 1 standard deviation below the mean?
Mean 72
First quartile 50
Median 68
Third quartile 75
Mode 70
92nd percentile 88
Standard Deviation 11
a. 61 b. 59 c. 57 d. 50