Question

1. the two - way frequency table shows the number of social media contacts for 7th - and 8th - graders.

	7th	8th	total
300 +	61	90	151
total	155	145	300

complete the column two - way relative frequency table.

	7th	8th	total
300 +	20%	62%	50%
total	40%	49%	100%

Explanation:

Step1: Calculate 0 - 300 for 8th

To find the relative frequency for 0 - 300 in 8th grade, we use the formula $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total of the column}}$. The frequency for 0 - 300 in 8th grade is 55, and the total for 8th grade column is 145. So, $\frac{55}{145}\approx0.379$ or 38% (rounded to the nearest whole number).

Step2: Calculate 300 + for 7th

For 300 + in 7th grade, the frequency is 61 and the total for 7th grade column is 155. So, $\frac{61}{155} = 0.3935\approx39\%$ (rounded to the nearest whole number).

Step3: Calculate Total for 7th

The total for 7th grade column is 155, and the overall total is 300. So, $\frac{155}{300}\approx0.5167\approx52\%$ (rounded to the nearest whole number).

Step4: Calculate Total for 8th

The total for 8th grade column is 145, and the overall total is 300. So, $\frac{145}{300}\approx0.4833\approx48\%$ (rounded to the nearest whole number). Wait, but let's check again with the column total. Wait, the column total for 7th is 155, so relative to column (7th column total is 155, so total relative frequency for 7th is $\frac{155}{155}=100\%$? Wait, no, column two - way relative frequency is relative to the column total. Oh! I made a mistake. Column two - way relative frequency: for each cell in a column, we divide by the column total.

Let's correct:

For 0 - 300, 8th grade:

Column total for 8th is 145. Frequency for 0 - 300 in 8th is 55. So relative frequency is $\frac{55}{145}\approx0.379 = 38\%$ (rounded to nearest whole number).

For 300 +, 7th grade:

Column total for 7th is 155. Frequency for 300 + in 7th is 61. So relative frequency is $\frac{61}{155}=0.3935\approx39\%$ (rounded to nearest whole number).

For Total, 7th grade:

Column total for 7th is 155, so $\frac{155}{155}=100\%$.

For Total, 8th grade:

Column total for 8th is 145, so $\frac{145}{145}=100\%$. Wait, but the overall total is 300. Wait, the problem says "column two - way relative frequency table", which means we calculate relative frequency with respect to the column total (not the grand total).

So let's redo:

0 - 300, 8th:

$\frac{55}{145}\approx0.379\approx38\%$

300 +, 7th:

$\frac{61}{155}=0.3935\approx39\%$

Total, 7th:

$\frac{155}{155}=100\%$

Total, 8th:

$\frac{145}{145}=100\%$

Wait, but the given table has "Total" row with 100% overall. But column two - way relative frequency: each column's total is 100% (since we divide by column total).

Let's check the first given cell: 0 - 300, 7th: $\frac{94}{155}=0.6065\approx61\%$ (which matches the given 61%).

So:

• 0 - 300, 8th: $\frac{55}{145}\approx0.379\approx38\%$
• 300 +, 7th: $\frac{61}{155}=0.3935\approx39\%$
• Total, 7th: $\frac{155}{155}=100\%$
• Total, 8th: $\frac{145}{145}=100\%$

Answer:

	7th	8th	Total
300 +	39%	62%	50%
Total	100%	100%	100%

(Note: The 50% in the "Total" row for 0 - 300 and 300 + is the overall relative frequency (relative to grand total 300), since 149/300≈0.4967≈50% and 151/300≈0.5033≈50%. The column relative frequencies are relative to column totals, and the "Total" row for the table (not column) is relative to grand total.)