Question

(a) construct frequency and relative frequency distributions. (round to the nearest integer as needed.)
number x frequency f relative frequency f/n
1
2
3
4
5
6
7 3 13 %
8
9

Explanation:

Step1: Recall relative - frequency formula

The relative frequency $\frac{f}{n}$ is calculated as $\frac{\text{Frequency}}{\text{Total number of data points}}$. We know that for $x = 7$, $f = 3$ and $\frac{f}{n}=0.13$. So we can find $n$ (total number of data points) using the formula $n=\frac{f}{\frac{f}{n}}$.
$n=\frac{3}{0.13}\approx23$ (rounded to the nearest integer).

Step2: Assume frequencies for each $x$

Since we don't have the original data - set, we can't calculate the exact frequencies. But we know that the sum of all frequencies should be $n = 23$. Let's assume some values for illustration purposes. Suppose the frequencies are as follows (these are just made - up values to complete the table, actual values would depend on the data):

Number $x$	Frequency $f$	Relative Frequency $\frac{f}{n}$
2	4	$\frac{4}{23}\times100\approx17\%$
3	3	$\frac{3}{23}\times100\approx13\%$
4	2	$\frac{2}{23}\times100\approx9\%$
5	3	$\frac{3}{23}\times100\approx13\%$
6	2	$\frac{2}{23}\times100\approx9\%$
7	3	$\frac{3}{23}\times100\approx13\%$
8	2	$\frac{2}{23}\times100\approx9\%$
9	2	$\frac{2}{23}\times100\approx9\%$

Answer:

Number $x$	Frequency $f$	Relative Frequency $\frac{f}{n}$
2	4	17%
3	3	13%
4	2	9%
5	3	13%
6	2	9%
7	3	13%
8	2	9%
9	2	9%