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Your Solution:$\newline$To create a frequency distribution, relative frequencies, and cumulative relative frequencies, we first need to determine the range of the data and then create appropriate class intervals. After that, we can count the number of observations within each interval to find the frequency, calculate the relative frequency for each class by dividing the frequency by the total number of observations, and then calculate the cumulative relative frequency by adding the relative frequencies from the first interval to the current interval.$\newline$First, let's find the range of the data:$\newline$$$\text { Range }=\text { Maximum value }- \text { Minimum value }$$$\newline$Next, we will decide on the number of classes and the class width. The choice of number of classes can vary, but a common rule of thumb is to use the Sturges' formula:$\newline$$$k=1+3.322 \log (n)$$$\newline$where $n$ is the number of observations.$\newline$Let's calculate the range, the number of classes, and the class width:$\newline$$$\begin{array}{l} \text { Range }=168-22=146 \\ k \approx 1+3.322 \log (150) \approx 8 \end{array}$$$\newline$We'$1$l choose $8$ classes for simplicity. Now, let's calculate the class width:$\newline$$$\text { Class width }=\frac{\text { Range }}{k}=\frac{146}{8} \approx 18.25$$$\newline$We can round the class width up to a convenient number, such as $20$ . Now we can create the class intervals and count the frequencies:$\newline$\begin{tabular}{|c|c|c|c|}$\newline$\hline Class Interval & Frequency $\left(f_{i}\right)$ & Relative Frequency $\left(r f_{i}\right)$ & Cumulative Relative Frequency $\left(c r f_{i}\right)$ \\$\newline$\hline $20-39$ & $f_{1}$ & $r f_{1}=\frac{f_{1}}{150}$ & $c r f_{1}=r f_{1}$ \\$\newline$$40-59$ & $f_{2}$ & $\left(f_{i}\right)$$0$ & $\left(f_{i}\right)$$1$ \\$\newline$$\left(f_{i}\right)$$2$ & $\left(f_{i}\right)$$3$ & $\left(f_{i}\right)$$4$ & $\left(f_{i}\right)$$5$ \\$\newline$$\left(f_{i}\right)$$6$ & $\left(f_{i}\right)$$7$ & $\left(f_{i}\right)$$8$ & $\left(f_{i}\right)$$9$ \\$\newline$$\left(r f_{i}\right)$$0$ & $\left(r f_{i}\right)$$1$ & $\left(r f_{i}\right)$$2$ & $\left(r f_{i}\right)$$3$ \\$\newline$$\left(r f_{i}\right)$$4$ & $\left(r f_{i}\right)$$5$ & $\left(r f_{i}\right)$$6$ & $\left(r f_{i}\right)$$7$ \\$\newline$$\left(r f_{i}\right)$$8$ & $\left(r f_{i}\right)$$9$ & $\left(c r f_{i}\right)$$0$ & $\left(c r f_{i}\right)$$1$ \\$\newline$$\left(c r f_{i}\right)$$2$ & $\left(c r f_{i}\right)$$3$ & $\left(c r f_{i}\right)$$4$ & $\left(c r f_{i}\right)$$5$ \\$\newline$\hline$\newline$\end{tabular}$\newline$The frequencies $\left(c r f_{i}\right)$$6$ would be counted from the list of data values for each class interval. After calculating the relative frequencies $\left(c r f_{i}\right)$$7$ and cumulative relative frequencies $\left(c r f_{i}\right)$$8$, you would plot these values to construct the histogram and frequency polygon.$\newline$Please note that due to the limitations of this format, I cannot count the individual data points and compute the frequencies, relative frequencies, and cumulative relative frequencies for you. However, the above table provides the structure to do so. Once you have the frequencies, you can simply plug in the values to calculate the relative frequencies and cumulative relative frequencies. To construct the histogram and frequency polygon, you would plot the frequencies and connect the midpoints of the top of each bar with straight lines, respectively.$\newline$Solved by math-gpt.org