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Sagot :
Let's analyze the provided frequency table to find answers to the given questions.
[tex]\[ \begin{tabular}{|r|r|r|c|c|c|} \hline \text{Lower} & \text{Upper} & f & cf & rf & crf \\ \hline 10 & 15 & 12 & 12 & 0.24 & 0.24 \\ \hline 16 & 21 & 6 & 18 & 0.12 & 0.36 \\ \hline 22 & 27 & 8 & 26 & 0.16 & 0.52 \\ \hline 28 & 33 & 8 & 34 & 0.16 & 0.68 \\ \hline 34 & 39 & 16 & 50 & 0.32 & 1.00 \\ \hline \end{tabular} \][/tex]
a. How many people are between 16 and 21 years of age?
To find this, we look at the frequency ([tex]\(f\)[/tex]) corresponding to the age range 16 to 21. According to the table, this frequency is 6.
Thus, the number of people between 16 and 21 years of age is:
[tex]\[ \boxed{6} \][/tex]
b. How many people are 21 years old or younger?
For this question, we need the cumulative frequency ([tex]\(cf\)[/tex]) up to the upper limit age of 21 years. This cumulative frequency is 18.
Hence, the number of people who are 21 years old or younger is:
[tex]\[ \boxed{18} \][/tex]
c. How many people are older than 21?
To find the number of people older than 21, we add the frequencies ([tex]\(f\)[/tex]) of the age ranges above 21:
[tex]\[ f(22 \text{ - } 27) + f(28 \text{ - } 33) + f(34 \text{ - } 39) = 8 + 8 + 16 \][/tex]
[tex]\[ = 32 \][/tex]
Thus, the number of people who are older than 21 is:
[tex]\[ \boxed{32} \][/tex]
d. What percent of people are 21 years old or younger? Enter a whole number.
We can refer to the cumulative relative frequency ([tex]\(crf\)[/tex]) corresponding to the cumulative frequency for ages up to 21. This value is 0.36. Converting to a percentage:
[tex]\[ 0.36 \times 100 = 36\% \][/tex]
Thus, the percent of people who are 21 years old or younger is:
[tex]\[ \boxed{36\%} \][/tex]
e. What percent of people are between 16 and 21 years of age? Enter a whole number.
To find the percent of people in this age range, we use the relative frequency ([tex]\(rf\)[/tex]) for ages 16 to 21. This value is 0.12. Converting to a percentage:
[tex]\[ 0.12 \times 100 = 12\% \][/tex]
Therefore, the percent of people between 16 and 21 years of age is:
[tex]\[ \boxed{12\%} \][/tex]
To summarize:
a. 6 people are between 16 and 21 years of age.
b. 18 people are 21 years old or younger.
c. 32 people are older than 21.
d. 36% of people are 21 years old or younger.
e. 12% of people are between 16 and 21 years of age.
[tex]\[ \begin{tabular}{|r|r|r|c|c|c|} \hline \text{Lower} & \text{Upper} & f & cf & rf & crf \\ \hline 10 & 15 & 12 & 12 & 0.24 & 0.24 \\ \hline 16 & 21 & 6 & 18 & 0.12 & 0.36 \\ \hline 22 & 27 & 8 & 26 & 0.16 & 0.52 \\ \hline 28 & 33 & 8 & 34 & 0.16 & 0.68 \\ \hline 34 & 39 & 16 & 50 & 0.32 & 1.00 \\ \hline \end{tabular} \][/tex]
a. How many people are between 16 and 21 years of age?
To find this, we look at the frequency ([tex]\(f\)[/tex]) corresponding to the age range 16 to 21. According to the table, this frequency is 6.
Thus, the number of people between 16 and 21 years of age is:
[tex]\[ \boxed{6} \][/tex]
b. How many people are 21 years old or younger?
For this question, we need the cumulative frequency ([tex]\(cf\)[/tex]) up to the upper limit age of 21 years. This cumulative frequency is 18.
Hence, the number of people who are 21 years old or younger is:
[tex]\[ \boxed{18} \][/tex]
c. How many people are older than 21?
To find the number of people older than 21, we add the frequencies ([tex]\(f\)[/tex]) of the age ranges above 21:
[tex]\[ f(22 \text{ - } 27) + f(28 \text{ - } 33) + f(34 \text{ - } 39) = 8 + 8 + 16 \][/tex]
[tex]\[ = 32 \][/tex]
Thus, the number of people who are older than 21 is:
[tex]\[ \boxed{32} \][/tex]
d. What percent of people are 21 years old or younger? Enter a whole number.
We can refer to the cumulative relative frequency ([tex]\(crf\)[/tex]) corresponding to the cumulative frequency for ages up to 21. This value is 0.36. Converting to a percentage:
[tex]\[ 0.36 \times 100 = 36\% \][/tex]
Thus, the percent of people who are 21 years old or younger is:
[tex]\[ \boxed{36\%} \][/tex]
e. What percent of people are between 16 and 21 years of age? Enter a whole number.
To find the percent of people in this age range, we use the relative frequency ([tex]\(rf\)[/tex]) for ages 16 to 21. This value is 0.12. Converting to a percentage:
[tex]\[ 0.12 \times 100 = 12\% \][/tex]
Therefore, the percent of people between 16 and 21 years of age is:
[tex]\[ \boxed{12\%} \][/tex]
To summarize:
a. 6 people are between 16 and 21 years of age.
b. 18 people are 21 years old or younger.
c. 32 people are older than 21.
d. 36% of people are 21 years old or younger.
e. 12% of people are between 16 and 21 years of age.
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