Statistics job "For AE only"

Descriptive Statistics

For the following frequency distribution, calculate the requested descriptive statistics:

X f

86 2

88 5

89 6

90 9

91 13

93 11

94 7

95 5

96 2

97 1

n = _____

Mean = _____

Mdn. = _____

Mode = _____

Range = _____

Q = _____

Variance = _____

sd = _____

Shape: _____________________________

N345: Online Version

Answers to Exercises: Block 3: Descriptive Statistics

Here’s what I got:

N = 61

Mean = 91.5

Mdn = 91

Mode = 91

Range=86-97 (I’d also accept “11,” although I think 86-97 gives you more information)

Q = 1.6875

Variance = 6.3875

sd = 2.53

Shape: “Normal”

To help you see how I got my answers (or to check my accuracy against your), these are the preliminary numbers I worked with:

Sum of f(x) = 5584

_

Sum of f(x-X)2 = 383.25

If you guys are like my on campus students, the one that drives you nuts is Q. In case you didn’t get Q = 1.6875, here’s how I came up with it:

a. I divided 61 by 4 and got 15.25. There are 15.25 scores in each quartile.

b. I counted up from the bottom until I got to the 15.25th score. Both the 15th and the 16th scores were 90, so the 15.25th score is also 90.

c. Q1 is halfway between the 15.25th score (90) and the 16th score (90). Therefore, Q1 = 90.

d. I counted down from the top until I got to the 15.25th score. The 15th score down from the top was 94. The 15.25th score down is a quarter of the way between the 15th and 16th score. A quarter of the way from 94 to 93 is 93.75. 93.75 is the bottom score in the top quartile. Q3 is halfway between that 15.25th score (93.75) and the 16th score (93). Q3, therefore, is 93.375. Get it?

e. Q = Q3 – Q1 Q = 93.375 – 90 Q = 1.6875

2 2

Some Extra Practice (plus answers) for Blocks 2 (Normal Distribution) and 3 (Descriptive Statistics)

Block 2: Normal Distribution

The following problems deal with a distribution with these characteristics:

Mean = 58.5

sd = 8.0

1. Fill in the Blanks for the following “tool skill” problems:

x z %ile

63 _____ _____

51 _____ _____

_____ -.63 _____

_____ 1.22 _____

_____ _____ 35

_____ _____ 62

2. What percent of subjects fall between the raw scores of 60 and 70?

3. What is the cut-off score if you want to recognize the top 25%?

4. What percent of individuals receive a score higher than 65?

5. What percent of individuals receive scores below 50?

Block 3: Descriptive Statistics

6. Calculate the requested statistics for the following distribution:

x f

25 1

26 3

27 3

28 6

29 3

30 4

31 5

32 3

33 3

34 4

35 2

36 2

37 1

N = _____

Mean = _____

Median = _____

Mode = _____

Range = _____

Variance = _____

sd = _____

Q = _____

Shape: _____

Appropriate Measure of Central Tendency: ________________

Appropriate Measure of Variability: __________________

7. Calculate the requested statistics for the

x f

14 2

15 5

16 6

17 3

18 2

19 2

20 2

21 1

22 1

N = _____

Mean = _____

Median = _____

Mode = _____

Range = _____

Variance = _____

sd = _____

Q = _____

Shape: ____________________

Appropriate Measure of Central Tendency: _____________

Appropriate Measure of Variability: ________________

Answers to Additional Problems:

1. x z %ile

63 .56 71.23

51 -.94 17.36

53.5 -.63 26.43

68.3 1.22 88.88

55.4 -.39 35

61.0 .31 62

2. 34.98%

3. 63.9

4. 20.9%

5. 24.46%

6. N = 40

Mean = 30.6

Median = 30.5

Mode = 28

Range = 25-37

Variance = 10.041

sd = 3.169

Q = 2.5

Shape = Normal (would accept “pointy”)

Appropriate Measure of Central Tendency: Mean = 30.6

Appropriate Measure of Variability: sd = 3.169

7. N = 24

Mean = 17.0

Median = 16

Mode = 16

Range = 14 – 22

Variance = 4.911

sd = 2.216

Q = 2.25

Shape: Pointy

Appropriate Measure of Central Tendency: Mean = 17.0

Appropriate Measure of Variability: Range = 14 – 22

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