ANSWERS OF EXERCISE IV
1.Can Sum of Squares (SS) ever have a value less than zero? Explain your answer.
SS can not be less than zero, since SS is summation of squared deviations. So it is always
greater than zero or equal to zero.
2. In general what does it mean for a sample to have a standard deviation of zero? Describe
the scores in such a sample.
If a sample has a standard deviation of zero, it means all the scores in the sample are same.
So their deviations are equal to zero. Or the sample has only one score
3. A professor administers a 5-point quiz to a class of 40 students. The professor calculates a
mean of 4.2 for the quiz with a standard deviation of 11.4. Although the mean is a reasonable
value, you should realize that standard deviation is not. Explain why the standard deviation is
not a reasonable value.
standard deviation must be in the interval between 0 and 5 since scores are change in this
interval. So standard deviation can not be equal to 11.4. if standard deviation is equal to
11.4 there must be negative score or score bigger than 5. this case is imposible because all
scores are between 0 and 5.
4. A population of N=15 scores has a standard deviation of 4.0. What is the variance for this
population?
Variance = 16
5. A sample of n=35 scores has variance of 100. What is the standard deviation for this
sample?
standard deviation=10
6. On an exam with μ=75, you obtain a score of X=80.
a. Would you prefer that the exam distribution had σ=2 or σ=10?
I would prefer σ=2 since my score will be extereme and it is well above the mean
b. If your score is X=70, would you prefer σ=2 or σ=10?
I would prefer σ=10 since my score will be average below the mean
7. Two samples are as follows:
Sample A: 7, 9, 10, 8, 9, 12
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Sample B: 13, 5, 9, 1, 17, 9
a. Just by looking at these data, which sample has more variability? Explain your answer
sample b because score 1 and 17 seem as extremes and more deviate from the
mean according to the other scores. So the data is more volatile
b. Compute the mean and the standard deviation for each sample.
For sample a mean 9.16 and the standard deviation 1.72
For sample a mean 9 and the standard deviation 5.65
c. In which sample is the mean more representative of its scores?
Sample a
8. Calculate SS, Variance, and standard deviation for the following population:
5, 0, 9, 3, 8, 5
SS=54 , Variance = 10.8 and standard deviation=3.28
9. Calculate SS, Variance, and standard deviation for the following sample:
4, 7, 3, 1, 5
SS=20 , Variance = 5 and standard deviation=2.23
10. For the following sample:
2, 8, 5, 9, 1, 6, 6, 3, 6, 10, 4, 12
a. Calculate the range, the semi-interquartile range, and the standard deviation
Range = 11 or 12 , the semi-interquartile range=2.25, and the standard deviation=3.30
b. Add 2 points to every score and then compute the range, the semi-interquartile range,
and the standard deviation. How is variability affected when a constant is added to
every score.
range, the semi-interquartile range, and the standard deviation are same as above.
range, the semi-interquartile range, and the standard deviation are measurements of
variability. Adding 2 points to every score does not change range, the semi-interquartile
range, and the standard deviation sinve the variability of the scores are still same.
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11. For the following sample of n=5 scores:
3, 11, 14, 7, 15
a. Sketch a histogram showing the sample distribution.
1.2
1
0.8
0.6
Seri 1
0.4
0.2
0
3
7
11
14
15
b. Locate the value of the sample mean in your sketch and make an estimate of the
sample standard deviation.
Mean=10 so sample standard deviation should be between 1 and 7.
c. Compute SS, variance, and standard deviation for the sample
SS=100, variance=25, and standard deviation=5
12. For the following population of N=6 scores:
8, 10, 4, 8, 5, 13
d. Sketch a histogram showing the population distribution.
2.5
2
1.5
Seri 1
1
0.5
0
4
5
8
10
13
e. Locate the value of the population mean in your sketch and make an estimate of the
standard deviation.
Mean=8 so sample standard deviation should be between 3 and 5.
f. Compute SS, variance, and standard deviation for the population
SS=60.85, variance=12.17, and standard deviation=3.28
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