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Chapter 1: Frequency Tables

Question 5

\begin{tabular}{|c|c|}
\hline
Ages & Number of students \\
\hline
[tex]$15-18$[/tex] & 5 \\
\hline
[tex]$19-22$[/tex] & 5 \\
\hline
[tex]$23-26$[/tex] & 5 \\
\hline
[tex]$27-30$[/tex] & 4 \\
\hline
[tex]$31-34$[/tex] & 3 \\
\hline
[tex]$35-38$[/tex] & 5 \\
\hline
\end{tabular}

Find the relative frequency for the class with a lower class limit of 27.

Relative Frequency [tex]$=$[/tex] [tex]$\square$[/tex] [tex]$\%$[/tex]

Give your answer as a percent, rounded to two decimal places.



Answer :

GinnyAnswer
Certainly! Let's solve the problem step by step:

1. Determine the Total Number of Students:
We need to sum up the number of students in each age group to find the total number of students.
[tex]\[ 5 + 5 + 5 + 4 + 3 + 5 = 27 \][/tex]
So, the total number of students is 27.

2. Find the Number of Students in the Age Group 27-30:
According to the table, the number of students in the 27-30 age group is 4.

3. Calculate the Relative Frequency:
The relative frequency of an age group is the number of students in that age group divided by the total number of students, multiplied by 100 to get the percentage.
[tex]\[ \text{Relative Frequency} = \left( \frac{\text{Number of students in age group 27-30}}{\text{Total number of students}} \right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{Relative Frequency} = \left( \frac{4}{27} \right) \times 100 \][/tex]

4. Compute the Result:
Performing the division and multiplication gives:
[tex]\[ \left( \frac{4}{27} \right) \times 100 = 14.81\% \][/tex]

So, the relative frequency for the class with lower class limit 27 is:
[tex]\[ \boxed{14.81 \%} \][/tex]

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