Friedrich Engelke
BBA WS 00/01
Problem Set 1
NOTE TO CHAPTER 2In this chapter we considered only cases in which the classes were of equal
width. You can draw a histogram even if the classes are of unequal
width by drawing the diagram so that the area of each rectangle is
proportional to the number of numbers in its interval.
EXERCISES
1.The temperatures in degrees Celsius each day over a three-week period were as follows: 17, 18,
20, 22, 21, 19, 16, 15, 18, 20, 21, 21, 22, 21, 19, 20, 19, 17, 16, 16, 17. Compute the mean,
median, and mode of these raw data, and, using two-degree intervals starting with 15-16
draw a frequency diagram.
Note:An interesting statistic is the mode. The mode (or modes) is (or are) the data that occur most frequently.
2.Calculate the same statistics as in Exercise 1 using all of the positive numbers that are perfect
squares and that are less than 1,000. (For the frequency diagram use these intervals: 1-100,
101-200, etc.
3.Calculate the mean, median, and standard deviation for these numbers: 5, 10, 6, 11, 0, 0, 0, 10.
4.Change the 11 in the previous exercise to 100 and calculate the new answers.
5.Here are scores on an English paper for 30 students:
58
80
93
67
86
88
94
92
54
80
79
84
80
90
98
76
72
84
89
63
66
69
90
95
94
99
94
69
76
84
Here are some chemistry scores for the same students:
76
89
96
81
92
94
96
96
74
88
88
91
89
94
99
86
84
91
93
79
81
82
94
97
96
99
96
82
86
91
Calculate the mean, median, and standard deviation for the two sets of scores.
6.In 1999 the mean U.S. gross income was $41,510, while the median income was $29,600. What
do you think is the significance of the fact that the mean is greater than the median?
7.Calculate the mean, median, and standard deviation for these lists:
(a)
(b)
(c)
(d)
(e)
(f)
0,
0,
1,
1,
2,
4,
0,
0,
-1,
0
3,
9,
1,
2,
0,
-1,
4,
16,
2,
4,
1,
0,
5,
25,
3,
6,
0
1
6,
36,
7
14
7,
49,
8
64
Solved Problems
(Problem Set #1)
1.
Mean = 18.81; median = 19; mode = 21
2.Mean = 336; median = 256. Each number is a mode, since all of the numbers occur an equal
number of times.
3.x = 5.25. x2 = 47.75. Standard deviation =  47.75 - 5.252 = 20.19 = 4.49; median = 5.5
4.The median is not changed: it is still 5.5. The mean and standard deviation become much larger:
mean = 16.375; standard deviation = 31.85.
5.
mean
σ
median
English
81.43
84
12.016
Chemistry
89.33
91
6.789
6.When a set of numbers contains a few numbers that are far above the mean, but no numbers
that are far below the mean, then the mean will tend to be higher than the median.
7.
mean
σ
median
(a)
4
4
(b)
22.667
(c)
2.6
2
2.41661
(d)
5.2
4
4.83322
(e)
0
0
0.70711
(f)
0
0
0.70711
16
2.58199
21.4683