a To calculate the relative frequencies we first need to know the total of all frequencies. In order to find it we should add all of the given frequencies together.
B
b Note that the probability of randomly selecting a person working in the Service category is the same as the relative frequency of working in the Service category.
A
a
U.S. Occupational Categories of Employed Workers
Occupational Category
Management, Professional, and Related
Service
Sales and Office
Natural Resources, Construction, Maintenance
Production, Transportation, and Material Moving
Number (thousands)
9773
2271
1456
289
177
Relative Frequency
9773/13 966≈ 0.7
2271/13 966≈ 0.16
1456/13 966≈ 0.1
289/13 966 ≈ 0.02
177/13 966 ≈ 0.01
B
bProbability: 227113 966≈ 0.16 Explanation: See solution.
Practice makes perfect
a We are given a table showing the number of people (in thousands) working in each occupational category according to the U.S. Bureau of Labor Statistics. We want to make a table showing the relative frequency for each occupational sector. Consider the given table.
U.S. Occupational Categories of Employed Workers
Occupational Category
Management, Professional, and Related
Service
Sales and Office
Natural Resources, Construction, Maintenance
Production, Transportation, and Material Moving
Number (thousands)
9773
2271
1456
289
177
To calculate the relative frequency for each occupational sector, we first need to know the total of the given frequencies. That will be the sum of the numbers of people working in each sector.
Now to calculate the relative frequencies we need to divide the number of people working in a particular sector (the frequency of working in this sector) by the total of the frequencies, 13 966. Let's do it!
U.S. Occupational Categories of Employed Workers
Occupational Category
Management, Professional, and Related
Service
Sales and Office
Natural Resources, Construction, Maintenance
Production, Transportation, and Material Moving
Number (thousands)
9773
2271
1456
289
177
Relative Frequency
9773/13 966≈ 0.7
2271/13 966≈ 0.16
1456/13 966≈ 0.1
289/13 966 ≈ 0.02
177/13 966 ≈ 0.01
Note that since the results are approximated they might not add up to 1, but if we add the fractions we will obtain 1.
b Now we want to find the probability that a randomly selected person works in the Service category. To do so we can use the previously obtained table. We will mark the column we are interested in.
U.S. Occupational Categories of Employed Workers
Occupational Category
Management, Professional, and Related
Service
Sales and Office
Natural Resources, Construction, Maintenance
Production, Transportation, and Material Moving
Number (thousands)
9773
2271
1456
289
177
Relative Frequency
9773/13 966≈ 0.7
2271/13 966≈ 0.16
1456/13 966≈ 0.1
289/13 966 ≈ 0.02
177/13 966 ≈ 0.01
Note that the previously found relative frequency is exactly our probability. Let's think about why it is true. If we wanted to calculate the probability we would divide the number of favorable outcomes, 2271, by the number of all possible outcomes, which is the sum of numbers from every category, 13 966.
P(service)=2271/13 966≈ 0.16
The result is exactly the same as relative frequency, because we divided the same values even though when we calculated the relative frequency we called them a different name. Here the number of favorable outcomes corresponds to frequency, and the number of all possible outcomes corresponds to the total of frequencies.
