Q19 Relative Frequencies for Compari... [FREE SOLUTION]

Chapter 2: Q19 (page 49)

Relative Frequencies for Comparisons. In Exercises 19 and 20, construct the relative frequency distributions and answer the given questions.
Oscar Winners Construct one table (similar to Table 2-9 on page 47) that includes relative frequencies based on the frequency distributions from Exercises 5 and 6, and then compare the ages of Oscar-winning actresses and actors. Are there notable differences?

Short Answer

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The relative frequency distribution is constructed as follows.

Ages (in years)	Relative frequency of the best actresses	Relative frequency of the best actors
20-29	33.33%	1.15%
30-39	39.08%	32.18%
40-49	16.09%	41.38%
50-59	3.45%	17.24%
60-69	5.75%	6.90%
70-79	1.15%	1.15%
80-89	1.15%

Although the frequency distributions of the ages of the actors and actresses look somewhat similar, a large number of actresses have received the Oscar at an early age, and a greater number of actors have won the Oscar at a later age.

Step by step solution

Given information

The grouped frequency distributions of the ages of the best actors and best actresses are provided.

Relative frequency

The relative frequency of a class interval in a grouped frequency distribution is obtained using the formula given below.

$Relative frequency of a class interval = \frac{Frequency of a class interval}{Sum of all frequencies} 脳 100 %$

Calculation

A combined relative frequency distribution table is to be constructed for the given frequency distributions.

The table below shows the frequencies of the ages of the best actresses.

Age (years) of the best actresses when the Oscar was won	Frequency
20-29	29
30-39	34
40-49	14
50-59	3
60-69	5
70-79	1
80-89	1

The sum of all frequencies is calculated below.

$Sum of all frequencies = 29 + 34 + 14 + 3 + 5 + 1 + 1 = 87$

Using the formula mentioned above, the relative frequencies for the different classes are calculated as shown below.

$Relative {freq}_{1} = \frac{29}{87} 脳 100 % = 33.33 % Relative {freq}_{2} = \frac{34}{87} 脳 100 % = 39.08 % Relative {freq}_{3} = \frac{14}{87} 脳 100 % = 16.09 % Relative {freq}_{4} = \frac{3}{87} 脳 100 % = 3.45 %$

$Relative {freq}_{5} = \frac{5}{87} 脳 100 % = 5.75 % Relative {freq}_{6} = \frac{1}{87} 脳 100 % = 1.15 % Relative {freq}_{7} = \frac{1}{87} 脳 100 % = 1.15 %$

The table below shows the frequencies of the ages of the best actors.

Age (years) of the best actors when the Oscar was won	Frequency
20-29	1
30-39	28
40-49	36
50-59	15
60-69	6
70-79	1

The sum of the frequencies is calculated below.

$Sum of all frequencies = 1 + 28 + 36 + 15 + 6 + 1 = 87$

Using the formula mentioned above, the relative frequencies for the different classes are calculated as shown below.

$Relative {freq}_{1} = \frac{1}{87} 脳 100 % = 1.15 % Relative {freq}_{2} = \frac{28}{87} 脳 100 % = 32.18 % Relative {freq}_{3} = \frac{36}{87} 脳 100 % = 41.38 % Relative {freq}_{4} = \frac{15}{87} 脳 100 % = 17.24 % Relative {freq}_{5} = \frac{6}{87} 脳 100 % = 6.90 % Relative {freq}_{6} = \frac{1}{87} 脳 100 % = 1.15 %$

The combined relative frequency table is obtained as follows.

Ages (in years)	Relative frequency of the best actresses	Relative frequency of the best actors
20-29	33.33%	1.15%
30-39	39.08%	32.18%
40-49	16.09%	41.38%
50-59	3.45%	17.24%
60-69	5.75%	6.90%
70-79	1.15%	1.15%
80-89	1.15%

Comparison

The majority of actresses were in the age interval of 30-39 years when they won the Oscar, while the majority of actors were in the age interval of 40-49 years when they won the Oscar.
The range of age for both actors and actresses isapproximately between 30-70 years.
A substantial number of actresses have won the Oscar at an early age as compared to the actors.
On the other hand, a greater number of actors, as compared to actresses, have won the Oscar after the age of 50 years.