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
84  86  83  85  87
x
5
The mean for Student A is 85
425
x
5
x  85
90  75  94  68  98
x
5
425
x
The mean for Student B is 85
5
x  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
Total
10
Step 2
10/5 = 2
Step 3:
  2  1.414
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.
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.
210  245  220  230  225
x
5
1130
x
5
x  226
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
210  245  220  230  225
x
5
1130
x
5
x  226
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
Total
670
Step 2
670/5 = 134
Step 3:
  134  11.576
The standard deviation of the weights is approximately
11.576 lb.
Answers to 11.2B
17. Q1 = 5.895, Q3 = 7.95
Q1
5.35
5.90
Median
6.98
Q3
7.95
9.50
Answers to 11.2B
18. Q1 = 198, Q3 = 254
Q1
172
198
Median
217.5
Q3
254
375
Answers to 11.2B
19. Q1 = 20, Q3 = 30
Q1
16
20
Median
25
Q3
30
33
Answers to 11.2B
20. Q1 = 26, Q3 = 36
Q1
24
26
Median
29
Q3
36
46
Answers to 11.2B
21. Q1 = 4.3, Q3 = 6.1
Q1
2.6
4.3
Median
5.2
Q3
6.1
8
Answers to 11.2B
22. Q1 = 995, Q3 = 1283
Q1
789
995
Median
1103
Q3
1283
1400
Have a good weekend!
No school on Monday due to Labor Day.
Classes will resume on Tuesday,
September 2.