# Deviation and Z-Scores

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

The sum of the deviations from the mean are always which of the following?
 a. the range b. the standard deviaiton total c. zero d. positive

2.

A national achievement test is administered annually to 9th graders. The test has a mean score of 100 and a standard deviation of 15. If John’s z-score is 1.20, what was his score on the test?
 a. 82 b. 88 c. 112 d. 118

3.

Given a mean raw score of 43 and a standard deviation of 3.47, what is the z-score for a raw score of 48?
 a. -1.44 b. 1.44 c. 0.69 d. -0.69

5.

Find the standard deviation of  4, 9, 11, 12, 17, 5, 8, 12, 14 assuming a normal distribution.
 a. 4.2 b. 3.7 c. 3.9 d. 11.1

6.

Find the standard deviation of  1, 1, 1, 4, 7, 7, 7.assuming a normal distribution.
 a. 1.7 b. 2.78 c. 3 d. 7.35

7.

What can be said about a set of data when its standard deviation is small (but not zero)?
 a. The data are far apart. b. All of the data have the same value. c. The mean of the data can never be zero d. The data are close together.

8.

The standard deviation of a normally distributed data set is 9. If 50 is 2 standard deviations below the average value of the set, what is the value of the mean?
 a. 59 b. 41 c. 68 d. 32

9.

Which of the following data sets has the smallest standard deviation?
 a. 51,52,52,50,50,53,49 b. 55,58,52,50,22,35,42 c. 37,41,33,31,12,24,43 d. 28,34,24,21,8,36,13,

10.

Sandra had the following scores on her Algebra tests this semester:  100, 85, 55, 95, 75, 100. How many scores are within one standard deviation of the mean?
 a. 3 b. 4 c. 5 d. 6

11.

Find the variance for the following set of numbers: {24, 20, 17, 31, 43}.
 a. 86 b. 27 c. 33.4 d. 29

12.

Find the variance for the following set of numbers: {7, 4, 5, 1, 3}.
 a. 0 b. 1.6 c. 4 d. 4.4

13.

Find the standard deviation to the nearest tenth for the set of numbers: {41, 60, 77, 11, 65}.
 a. 10.3 b. 23 c. 50.8 d. 63.5

14.

Find the variance and standard deviation for the data set: {19, 28, 39, 44} .
 a. variance= 94.25     standard deviation=9.7 b. variance= 90.75     standard deviation=9.53 c. variance=210.5      standard deviation=14.51 d. variance=130         standard deviation=11.4

15.

Find the z-score corresponding to a raw score of 132 from a normal distribution with mean 100 and standard deviation 15.
 a. -1.17 b. 1.17 c. -2.133 d. 2.133

16.

A z-score of 1.7 was found from a normal distribution with mean 14 and standard deviation 3. Find the raw score.
 a. 8.9 b. 15.7 c. 19.1 d. 47.1

17.

Calculate the z-score for blood pressure of 140 with a sample mean of 110 and standard deviation of 10.
 a. -3 b. -1.4 c. 1.4 d. 3

18.

Calculate the z-score for blood pressure of 130 with a sample mean of 120 and standard deviation of 20.
 a. -1.5 b. -0.5 c. 0.5 d. 1.5

19.

Suppose that SAT scores among seniors are normally distributed with a mean of 500 and a standard deviation of 80. Find the z value for an SAT score of 300.
 a. -2.5 b. -0.4 c. 0.4 d. 2.5

20.

Suppose that SAT scores among seniors are normally distributed with a mean of 500 and a standard deviation of 60. Find the z value for an SAT score of 680.
 a. -3 b. -1.33 c. 1.33 d. 3

21.

Jason found the standard deviation of this set of numbers : {3, 6, 2, 1, 7, 5}. If he adds 5 to each of the numbers in the data set, how will the standard deviation change?
 a. no change b. increases by 5 c. decreases by 5 d. increases by 1

22.

A caterer must hire waiters as needed for private parties. Given are the number of employees hired each month for a five month period:   4, 13, 5, 6, 9 . What is the population standard deviation for this data?
 a. 3.3 b. 7.4 c. 10.8 d. 13.5

23.

In a population of scores, a raw score of 48 has a z-score of 1 and a raw score of 53 has a z-score of 2. What is the standard deviation of this population?
 a. 5 b. -5 c. 10 d. -10

24.

In a population of scores, a raw score of 72 has a z-score of 1 and a raw score of 76 has a z-score of 2. What is the mean of this population?
 a. -4 b. 4 c. 68 d. 80

25.

Find the mean absolute deviation of this set: {85, 90, 68, 75, 79}.
 a. 1.92 b. 6.48 c. 32.4 d. 79.4

26.

While decorating her bedroom, Sandra spent the following amounts: \$29, \$58, \$15, \$129, \$75, and \$22. Find the mean absolute deviation for her expenses.
 a. 32.7 b. 54.7 c. 114 d. 196

27.

Two families have 8 people in each. Given the ages in each family, which statement best describes the variability of the two families.
Family A:  35, 5, 42, 9, 16, 3, 8, 12                 Family B:  1, 5, 29, 3, 7, 35, 6, 9
 a. The variability is the same for both families because they have the same mean absolute deviations. b. Family A has the greater variability because their mean absolute deviation is the greatest. c. Family B has the greater variability because their mean absolute deviation is the greatest. d. There is not enough information to determine the variability.

28.

Find the mean absolute deviation for the following set: {65, 90, 85, 70, 70, 95, 50}.
 a. 7.1 b. 10 c. 12.9 d. 90

29.

Given forecast errors of -1, 4, 8 and -3, what is the mean absolute deviation?
 a. 2 b. 3 c. 4 d. 8

30.

Determine the mean absolute deviation of the following weights of five team members:  56 kg, 78 kg, 90 kg, 82 kg, 94kg,
 a. 9.6 b. 10 c. 13.3 d. 80

Answers:(1C 2D 3B 5C 6B 7D 8C 9A 10C 11A 12C 13B 14A 15D 16C 17D 18 C 19A 20D 21A 22A 23A 24C 25B  26A 27B 28C 29C 30C)

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