Chapter 2
Summarizing and Graphing Data
2-2
Frequency Distributions
1. No.
The first class frequency, for example, tells us only that there were 18 pennies with
weights in the 2.40-2.49 grams class, but there is no way to tell the exact values of those 18
weights.
2. The sum of the relative frequencies should be 1.00 when proportions are used, and it should be
100% when percentages are used.
3. No. This is not a relative frequency distribution because the sum of the percentages is not
100%.
It appears that each respondent was asked to indicate whether he downloaded the four
types of material (and so the sum of the percentages could be anywhere
from 0% to 400%),
and not to place himself in one of the four categories (in which case the table would be a
relative frequency distribution and the sum of the percentages would be 100%).
4. The gap in the frequencies suggests the table includes heights from two different populations.
Considering the values, it appears that the two populations are elementary students and
faculty/staff personnel at the school.
5. a. Class width: subtracting the first two lower class limits, 14
−
10 = 4.
b. Class midpoints: the first class midpoint is (10+13)/2 = 11.5, and the others can be obtained
by adding the class width to get 11.5, 15.5, 19.5, 23.5, 27.5.
c. Class boundaries: the boundary between the first and second class is (13+14)/2 = 13.5, and
the others can be obtained by adding or subtracting the class width to get 9.5, 13.5, 17.5,
21.5, 25.5, 29.5.
6. a. Class width: subtracting the first two lower class limits, 6
−
2 = 4.
b. Class midpoints: the first class midpoint is (2+5)/2 = 3.5, and the others can be obtained by
adding the class width to get 3.5, 7.5, 11.5, 15.5.
c. Class boundaries: the boundary between the first and second class is (5+6)/2 = 5.5, and the
others can be obtained by adding or subtracting the class width to get 1.5, 5.5, 9.5, 13.5,
17.5.
7. a. Class width: subtracting the first two lower class limits, 1.00
−
0.00 = 1.00.
b. Class midpoints: the first class midpoint is (0.00+0.99)/2 = 0.495, and the others can be
obtained by adding the class width to get 0.495, 1.495, 2.495, 3.495, 4.495.
c. Class boundaries: the boundary between the first and second class is (0.99+1.00)/2 = 0.995,
and the others can be obtained by adding or subtracting the class width to get -0.005, 0.995,
1.995, 2.995, 3.995, 4.995.
8. a. Class width: subtracting the first two lower class limits, 1.00
−
0.00 = 1.00.
b. Class midpoints: the first class midpoint is (0.00+0.99)/2 = 0.495, and the others can be
obtained by adding the class width to get 0.495, 1.495, 2.495, 3.495, 4.495, 5.495
c. Class boundaries: the boundary between the first and second class is (0.99+1.00)/2 = 0.995,
and the others can be obtained by adding or subtracting the class width to get -0.005, 0.995,
1.995, 2.995, 3.995, 4.995, 5.995.