11.2C Standard Deviation Statistics Mrs. Spitz Fall 2009

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

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

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

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.

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.

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

Step 2 10/5 = 2

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

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.

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

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 = (245 – 226)(19) 2 = (220 – 226)(-6) 2 = (230 – 226)(4) 2 = (225 – 226)(-1) 2 = 1 Total670

Step 2 670/5 = 134

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

Answers to 11.2B 17. Q1 = 5.895, Q3 = Q1Q1 Q3Q3 Median

Answers to 11.2B 18. Q1 = 198, Q3 = Q1Q1 Q3Q3 Median

Answers to 11.2B 19. Q1 = 20, Q3 = Q1Q1 Q3Q3 Median

Answers to 11.2B 20. Q1 = 26, Q3 = Q1Q1 Q3Q3 Median

Answers to 11.2B 21. Q1 = 4.3, Q3 = Q1Q1 Q3Q3 Median

Answers to 11.2B 22. Q1 = 995, Q3 = Q1Q1 Q3Q3 Median

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