Answers to Problems for Topic 1
1. Although some variables can be measured in several ways, the
most
likely is indicated.
1. Age Continuous
2. Ethnic origin Categorical no order
3. Source of drinking water Categorical no order
4. Level of education Categorical with order
5. Height Continuous
6. Exposure to lead Continuous
7. Level of cholesterol Continuous
8. Political orientation Categorical with order
9. Political affiliation Categorical no order
10. Income Continuous
11. Occupation Categorical no order
12. Attitude toward statistics Categorical with order
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2a. Mode
There is only one value with a freuqency greater than 1. This
is 8. The mode is 8.
Median
Rank the values
1 2 3 4 5 6 8 8 11 12
There are ten values. The median is the average of the fifth and
sixth. It equals (5+6)/2 = 5.5.
Mean
The mean equals (1+2+3+4+5+6+8+8+11+12)/10 = 60/10 = 6.0.
2b. The range is the largest value minus the smallest = 12 - 1 =
11.
The variance equals (25+16+9+4+1+0+4+4+25+36)/9 = 124/9=13.78.
The
standard deviation equals sqrt(13.78) = 3.71.
Return to the questions.
3a. The mode equals the most frequent score which is 3 with a
frequency of 7.
The information needed to compute the mean and median is
Score freq Percent Cum Percent Score x freq
1 4 16.0 16.0 1 x 4 = 4
2 5 20.0 36.0 2 x 5 = 10
3 7 28.0 64.0 3 x 7 = 21
4 5 16.0 80.0 4 x 5 = 20
5 4 20.0 100.0 5 x 4 = 20
Total 25 100.0 75
The median is 3 because 50% of the distribution falls in the
group of three's. The mean is 75/25 = 3.0.
3b. The range equals 5 - 1 = 4.
x Freq x - Mean (x - Mean)sq dev sq x f
1 4 -2 4 16
2 5 -1 1 5
3 7 0 0 0
4 5 1 1 5
5 4 2 4 16
Total 42
The variance equals 42/24 = 1.75. The standard deviation
equals 1.32.
Return to the questions.
4a. The mode is 3 with a frequency of 7.
The information needed to compute the mean and the median is
shown below.
Score Frequency Cum % score x f
1 3 12 3
2 6 36 12
3 7 64 21
4 3 76 12
5 2 84 10
6 2 92 12
7 1 96 7
8 1 100 8
Total 25 85
The median is 3. The mean equals 85/25 = 3.4. It is slightly
larger than the median because the distribution is slightly
skewed
to the right.
4b. The range is 8 - 1 = 7.
The variance equals (3 x 5.76 + 6 x 1.96 + 7 x .16 + 3 x .36 +
2 x 2.56 + 2 x 6.76 + 12.96 + 21.16)/24 = 3.5. The standard
deviation equals sqrt(3.5) = 1.87.
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