Answer :
We begin by noting that the heights range from a minimum of [tex]$138$[/tex] cm to a maximum of [tex]$166$[/tex] cm. Since the data covers these values, we can create class intervals of width [tex]$5$[/tex] cm that conveniently include all values. One appropriate set of intervals is:
[tex]$$
138-142,\quad 143-147,\quad 148-152,\quad 153-157,\quad 158-162,\quad 163-167.
$$[/tex]
The next step is to count how many student heights fall into each interval.
1. For the interval [tex]$138$[/tex]–[tex]$142$[/tex], there are [tex]$5$[/tex] students.
2. For the interval [tex]$143$[/tex]–[tex]$147$[/tex], there are [tex]$9$[/tex] students.
3. For the interval [tex]$148$[/tex]–[tex]$152$[/tex], there are [tex]$18$[/tex] students.
4. For the interval [tex]$153$[/tex]–[tex]$157$[/tex], there are [tex]$12$[/tex] students.
5. For the interval [tex]$158$[/tex]–[tex]$162$[/tex], there are [tex]$5$[/tex] students.
6. For the interval [tex]$163$[/tex]–[tex]$167$[/tex], there are [tex]$7$[/tex] students.
Now, we can present the grouped frequency table as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\textbf{Height Interval (cm)} & \textbf{Frequency} \\
\hline
138\text{--}142 & 5 \\
143\text{--}147 & 9 \\
148\text{--}152 & 18 \\
153\text{--}157 & 12 \\
158\text{--}162 & 5 \\
163\text{--}167 & 7 \\
\hline
\end{array}
\][/tex]
This table efficiently summarizes the distribution of heights for the [tex]$56$[/tex] students.
[tex]$$
138-142,\quad 143-147,\quad 148-152,\quad 153-157,\quad 158-162,\quad 163-167.
$$[/tex]
The next step is to count how many student heights fall into each interval.
1. For the interval [tex]$138$[/tex]–[tex]$142$[/tex], there are [tex]$5$[/tex] students.
2. For the interval [tex]$143$[/tex]–[tex]$147$[/tex], there are [tex]$9$[/tex] students.
3. For the interval [tex]$148$[/tex]–[tex]$152$[/tex], there are [tex]$18$[/tex] students.
4. For the interval [tex]$153$[/tex]–[tex]$157$[/tex], there are [tex]$12$[/tex] students.
5. For the interval [tex]$158$[/tex]–[tex]$162$[/tex], there are [tex]$5$[/tex] students.
6. For the interval [tex]$163$[/tex]–[tex]$167$[/tex], there are [tex]$7$[/tex] students.
Now, we can present the grouped frequency table as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\textbf{Height Interval (cm)} & \textbf{Frequency} \\
\hline
138\text{--}142 & 5 \\
143\text{--}147 & 9 \\
148\text{--}152 & 18 \\
153\text{--}157 & 12 \\
158\text{--}162 & 5 \\
163\text{--}167 & 7 \\
\hline
\end{array}
\][/tex]
This table efficiently summarizes the distribution of heights for the [tex]$56$[/tex] students.
