Measures of Dispersion 7-6 Statistics Measures of Dispersion

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

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

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

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.

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.

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.

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

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

Example (continued), mean = 514 The standard deviation is $290.35.

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

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

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

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

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

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

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%

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%

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%

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%

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. 1360 b. 1400 c. 1440 d. 1500

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. 1360 b. 1400 c. 1440 d. 1500

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. 84.5 c. 86.5 d. 88.5

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. 84.5 c. 86.5 d. 88.5

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

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