1. 11.2C Standard Deviation Statistics Mrs. Spitz Fall 2009

2. Objectives Student should be able to compute standard deviation given data. Student will be able to interpret what the standard deviation means in a given problem. Assignment 11.2C

3. Introduction Consider two students, each of whom has taken five exams. Student A has scores 84, 86, 83, 85, and 87. Student B has scores 90, 75, 94, 68, and 98. Compute the mean for both Student A and Student B

4. Computing the mean The mean for Student A is 85 The mean for Student B is 85

5. And... For each of these students, the mean (average) of 5 tests is 85. However, Student A has a more consistent record of scores than Student B. One way to measure the consistency or “clustering” of data near the mean is the standard deviation.

6. To calculate the standard deviation 1.Sum the squares of the differences between each value of data and the mean. 2.Divide the result in Step 1 by the number of items in the set of data. 3.Take the square root of the result in Step 2.

7. Here is the calculation for Student A. The symbol for standard deviation is the Greek letter sigma, denoted by  -- This is Step 1 x(x – x)(x – x) 2 84(84 – 85)(-1) 2 = 1 86(86 – 85)(1) 2 = 1 83(83 – 85)(-2) 2 = 4 85(85 – 85)(0) 2 = 0 87(87 – 85)(2) 2 = 4 Total10

8. Step 2 10/5 = 2

9. Step 3: The standard deviation for Student A’s score is approximately 1.414. Following a similar procedure for Student B, the standard deviation for Student B’s score is approximately 11.524. Since the standard deviation of Student B’s scores is greater than that of Student A’s (11.524 > 1.414), Student B’s scores are not as consistent as those of Student A.

10. The weights in pounds of the five-man front line of a college football team are 210, 245, 220, 230, and 225. find the standard deviation of the weights. To calculate standard deviation: –Find the mean of the weights –Use the procedure for calculating standard deviation.

11. The weights in pounds of the five-man front line of a college football team are 210, 245, 220, 230, and 225. find the standard deviation of the weights. To calculate standard deviation: –Find the mean of the weights

12. Here is the calculation for Student A. The symbol for standard deviation is the Greek letter sigma, denoted by  -- This is Step 1 x(x – x)(x – x) 2 210(210 – 226)(-16) 2 = 256 245(245 – 226)(19) 2 = 361 220(220 – 226)(-6) 2 = 36 230(230 – 226)(4) 2 = 16 225(225 – 226)(-1) 2 = 1 Total670

13. Step 2 670/5 = 134

14. Step 3: The standard deviation of the weights is approximately 11.576 lb.

15. Answers to 11.2B 17. Q1 = 5.895, Q3 = 7.95 5.355.90 6.987.95 9.50 Q1Q1 Q3Q3 Median

16. Answers to 11.2B 18. Q1 = 198, Q3 = 254 172198 217.5254 375 Q1Q1 Q3Q3 Median

17. Answers to 11.2B 19. Q1 = 20, Q3 = 30 1620 2530 33 Q1Q1 Q3Q3 Median

18. Answers to 11.2B 20. Q1 = 26, Q3 = 36 2426 2936 46 Q1Q1 Q3Q3 Median

19. Answers to 11.2B 21. Q1 = 4.3, Q3 = 6.1 2.64.3 5.26.1 8 Q1Q1 Q3Q3 Median

20. Answers to 11.2B 22. Q1 = 995, Q3 = 1283 789995 11031283 1400 Q1Q1 Q3Q3 Median

21. Have a good weekend! No school on Monday due to Labor Day. Classes will resume on Tuesday, September 2.