Describing Data – Odd Numbers Only
Example 5
VADS customer service counts all the number of incoming calls per day during the first 7 days in May
14
24
19
31
36
26
17
a. Compute the mean.
b. Is this a statistic or a parameter? Why?
Giant Hypermarket began a study of overtime hours among its workers. A sample of 15 workers showed the following overtime hours last month
13
13
12
15
7
15
5
12
6
7
12
10
9
13
12
a. Compute the mean.
b. Is this a statistic or a parameter? Why?
Example 6
The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of coursework, a student at State University earned 9 credit hours of A, 15 credit hours of B, 33 credit hours of C, and 3 credit hours of D.
a. Compute the student’s grade point average (GPA).
b. If the minimum requirement to be admitted into the business college is a 2.5 GPA for their first 60 credit hours of coursework, will this student be admitted?
Example 7
a. Calculate the geometric mean percent increase.
b. Calculate the arithmetic mean percent increase.
c. Based on (a) and (b), what is the relationship between geometric mean and arithmetic mean?
Example 8
Below are the costs for a year of college in public and private colleges in 1992 and 2007. What is the geometric mean annual increase for the period for the two types of colleges? Compare the rates of increase.
Type of college
1992
2007
Public
$ 4,975
$11,354
Private
12,284
27,516
Example 9
A company’s HR department was interested in the average number of years that a person works before retiring. A sample of workers shared their remaining years of service:
10
16
18
19
20
21
21
22
24
24
24
a. What is the mode? What does it signify?
b. What is the arithmetic mean? Interpret its meaning.
c. What is the median? Explain this value.
Example 10
Below are starting admission price (in RM) for one-day tickets to 10 theme parks around the Klang Valley:
58 63 41 42 29 50 62 43 40 40
a. Compute the mean, median and mode.
b. Based on the results of (a), what conclusion can you reach concerning the distribution of the starting admission price for one-day tickets?
Example 11
Two machines, A and B, are used to pack biscuits. A sample of 10 packets was taken from each machine and the mass of each packet, measured to the nearest gram, was noted. Find the standard deviation of the masses of the packets taken in the sample from each machine. Which machine, do you think, is more
reliable? Explain your answer.
Machine A (mass in g)
196
198
198
199
200
200
201
201
202
205
Machine B (mass in g)
192
194
195
198
200
201
203
204
206
207
Example 12
The age distribution of a sample of 5000 people is bell-shaped with a mean of 40 years and a standard deviation of 12 years. Determine the approximate percentage of people who are 16 to 64 years old.
Example 13
Below are the graphs of two symmetrical curves. Answer the following:
a. Which curve has the larger standard deviation?
b. What is the mean for graph A?
c. If the standard deviation of Graph A is 2.5, using the Empirical Rule, about 95% of the observations fall within what two values?
Example 14
The mean income for a sample of 75 part-time assistants at IIUM is RM800 and the standard deviation is RM40.
a. According to Chebyshev’s theorem, at least what percent of the income will lie between RM600 and RM1000?
b. How many of the part-time assistants will receive the income between RM600 and RM1000?
Example 15
Suppose a distribution has a mean of 111 and standard deviation of 7.6. If Chebyshev’s Theorem tells us that 81.1% of the values are between a and b (symmetrical about the mean), then what are these values?
Example 16
A sample of five clerks revised the following number of tax records in the last hour: 73, 98, 60, 92 and 84. Compute the coefficient of skewness using the Pearson method. What is your conclusion regarding the shape of the distribution?
4