Question

number x frequency f relative frequency $\frac{f}{n}$ data table full data set 7 9 2 4 5 7 9 2 4 6 8 9 2 5 6 9 1 2 5 7 9 2 3 5

Explanation:

Step1: Count total data points

Count the number of values in the full - data set. There are 30 values, so $n = 30$.

Step2: Calculate frequencies for known values

For $x = 4$, frequency $f = 2$. For $x = 6$, frequency $f = 2$. For $x = 7$, frequency $f = 3$.

Step3: Calculate remaining frequencies

Count the number of 1s, 2s, 3s, 5s, 8s, and 9s in the data set:

• Number of 1s: 1, so frequency of 1 is 1.
• Number of 2s: 5, so frequency of 2 is 5.
• Number of 3s: 2, so frequency of 3 is 2.
• Number of 5s: 5, so frequency of 5 is 5.
• Number of 8s: 1, so frequency of 8 is 1.
• Number of 9s: 6, so frequency of 9 is 6.

Step4: Calculate relative frequencies

Relative frequency of $x$ is $\frac{f}{n}\times100\%$.

• For $x = 1$: $\frac{1}{30}\times100\%\approx3.33\%$
• For $x = 2$: $\frac{5}{30}\times100\%\approx16.67\%$
• For $x = 3$: $\frac{2}{30}\times100\%\approx6.67\%$
• For $x = 4$: $\frac{2}{30}\times100\%\approx6.67\%$
• For $x = 5$: $\frac{5}{30}\times100\%\approx16.67\%$
• For $x = 6$: $\frac{2}{30}\times100\%\approx6.67\%$
• For $x = 7$: $\frac{3}{30}\times100\% = 10\%$ (already given as 13% in the problem, but our calculation based on data is 10%)
• For $x = 8$: $\frac{1}{30}\times100\%\approx3.33\%$
• For $x = 9$: $\frac{6}{30}\times100\% = 20\%$

The completed table:

Number $x$	Frequency $f$	Relative Frequency $\frac{f}{n}\%$
2	5	16.67
3	2	6.67
4	2	6.67
5	5	16.67
6	2	6.67
7	3	10
8	1	3.33
9	6	20

Answer:

Number $x$	Frequency $f$	Relative Frequency $\frac{f}{n}\%$
2	5	16.67
3	2	6.67
4	2	6.67
5	5	16.67
6	2	6.67
7	3	10
8	1	3.33
9	6	20