For each of the following data sets find the following. In an excel spread sheet
ID: 3363877 • Letter: F
Question
For each of the following data sets find the following.
In an excel spread sheet
The following note on the original assignment sheet contains an erroneous statement:
You can use the Data Analysis Toolpak (Descriptive Statistics) for most of the calculations, but you’ll need VAR and STDEV functions to calculate the unbiased estimates.
Wrong! The Data Analysis Toolpak gives you the unbiased estimates automatically as part of its output. What it should say is:
You can use the Data Analysis Toolpak (Descriptive Statistics) for most of the calculations, but you’ll need VAR.P and STDEV.P functions to calculate the variance and standard deviation for describing the data.
Mean
Median
Mode
Range
Variance (for describing the data)
Standard deviation (for describing the data)
The unbiased estimate of the variance
The unbiased estimate of the standard deviation
Data Set A Data Set B Data Set C
Scores on a Math Test Scores on English Test Scores on a Test of
Spatial Ability
78 88 100
47 90 124
73 87 104
88 82 98
97 81 104
92 80 108
78 88 98
80 82 84
69 82 84
76 92 110
Describe the normal curve.
C ompute the z scores for the following raw scores where X = 72 and the standard deviation = 12.
63
84
EXTRA CREDIT
Using a distribution with a mean of 500 and a standard deviation of 100.
What is the percentile score of a score of 640?
What is the percentile score of a score of 440?
ANSWERS BEGIN ON THE NEXT PAGE
1. Descriptive statistics
A - Math
B - English
C - Spatial
77.8
85.2
101.4
Mean
78
84.5
102
Median
78
82
104
Mode
50
12
40
Range
173.16
16.36
127.24
Variance-data (VAR.P)
13.16
4.04
11.28
SD - data (STDEV.P)
192.4
18.18
141.38
Variance - unbiased (VAR.S)
13.87
4.26
11.89
SD - unbiased (STDEV.S)
2. Describe the normal curve.
See Chapter 14 in the research methods book and/or Chapter 8 in the statistics book.
3. C ompute the z scores for the following raw scores where X = 72 and the standard deviation = 12.
A. 63
B. 84
Raw score (X)
Z score
63
-0.75
84
1.00
EXTRA CREDIT
4. Using a distribution with a mean of 500 and a standard deviation of 100.
A. What is the percentile score of a score of 640?
B. What is the percentile score of a score of 440?
(Hint: convert the raw score to z, and use Excel’s NORM.S.DIST function or the online normal curve calculator athttp://davidmlane.com/hyperstat/z_table.html .)
Raw Score
z
Percentile*
640
1.4
0.919
440
-0.6
0.274
* Technically this should be “Percentile Rank,” but we often just say “Percentile.”
(See next page for what these look like if you use the online calculator.
Percentile for z = +1.4:
Note that the black portion of the graph shows the 91.92% below (to the left of) z = +1.4
Percentile for z = -0.6
Note that the black portion of the graph shows the 27.43% below z = -0.6
4
The following note on the original assignment sheet contains an erroneous statement:
You can use the Data Analysis Toolpak (Descriptive Statistics) for most of the calculations, but you’ll need VAR and STDEV functions to calculate the unbiased estimates.
Wrong! The Data Analysis Toolpak gives you the unbiased estimates automatically as part of its output. What it should say is:
You can use the Data Analysis Toolpak (Descriptive Statistics) for most of the calculations, but you’ll need VAR.P and STDEV.P functions to calculate the variance and standard deviation for describing the data.
Explanation / Answer
Result:
A - Math
B - English
C - Spatial
77.8
85.2
101.4
Mean
78
84.5
102
Median
78
82
104
Mode
50
12
40
Range
173.16
16.36
127.24
Variance-data (VAR.P)
13.16
4.04
11.28
SD - data (STDEV.P)
192.4
18.18
141.38
Variance - unbiased (VAR.S)
13.87
4.26
11.89
SD - unbiased (STDEV.S)
2. Describe the normal curve.
Normal distributions are symmetric around their mean.
The mean, median, and mode of a normal distribution are equal.
The area under the normal curve is equal to 1.0.
Normal distributions are denser in the center and less dense in the tails.
Normal distributions are defined by two parameters, the mean () and the standard deviation ().
68% of the area of a normal distribution is within one standard deviation of the mean. Approximately 95% of the area of a normal distribution is within two standard deviations of the mean. Approximately 99.7% of the area of a normal distribution is within three standard deviations of the mean.
3. Compute the z scores for the following raw scores where X = 72 and the standard deviation = 12.
A. 63
B. 84
Raw score (X)
Z score
63
-0.75
84
1.00
EXTRA CREDIT
4. Using a distribution with a mean of 500 and a standard deviation of 100.
A. What is the percentile score of a score of 640?
B. What is the percentile score of a score of 440?
Raw Score
z
Percentile*
640
1.4
0.919
440
-0.6
0.274
Percentile for z = +1.4: Note that the black portion of the graph shows the 91.92% below (to the left of) z = +1.4
Percentile for z = -0.6: Note that the black portion of the graph shows the 27.43% below z = -0.6
A - Math
B - English
C - Spatial
77.8
85.2
101.4
Mean
78
84.5
102
Median
78
82
104
Mode
50
12
40
Range
173.16
16.36
127.24
Variance-data (VAR.P)
13.16
4.04
11.28
SD - data (STDEV.P)
192.4
18.18
141.38
Variance - unbiased (VAR.S)
13.87
4.26
11.89
SD - unbiased (STDEV.S)
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