the two-way table shows the number of students that do or do not do chores at home and whether they receive an allowance or not. find and interpret the relative frequencies of students in the survey by columns.

allowance no allowance total
chores- 13;13/16- 3;3/16- 16; 16/32
no chores- 5;5/9- 4; 4/9- 9;9/18
total- 18; / - 7; / - 25; /

Quick check answers for Unit 2 Lesson 2 frequency is:

B
B
D
D

100% hope this helps anyone!

It did thx

##
__

To find the relative frequencies of students in the survey by columns, we need to calculate the proportions of students within each column.

For the "Allowance" column:
- The total number of students who receive an allowance is 18.
- To find the relative frequency for "Chores" and "Allowance," we divide the number of students who do chores and receive an allowance by the total number of students who receive an allowance: 13/18 = 0.722
- To find the relative frequency for "No Chores" and "Allowance," we divide the number of students who do not do chores and receive an allowance by the total number of students who receive an allowance: 5/18 = 0.278

For the "No Allowance" column:
- The total number of students who do not receive an allowance is 7.
- To find the relative frequency for "Chores" and "No Allowance," we divide the number of students who do chores and do not receive an allowance by the total number of students who do not receive an allowance: 3/7 ≈ 0.429
- To find the relative frequency for "No Chores" and "No Allowance," we divide the number of students who do not do chores and do not receive an allowance by the total number of students who do not receive an allowance: 4/7 ≈ 0.571

In summary:
- For the "Allowance" column, the relative frequency of students who do chores and receive an allowance is approximately 0.722, and the relative frequency of students who do not do chores and receive an allowance is approximately 0.278.
- For the "No Allowance" column, the relative frequency of students who do chores and do not receive an allowance is approximately 0.429, and the relative frequency of students who do not do chores and do not receive an allowance is approximately 0.571.

Interpretation:
The relative frequencies calculated show the proportion of students within each column (allowance or no allowance) who fall into the two categories (chores or no chores).
In the "Allowance" column, approximately 72.2% of students who receive an allowance do chores, while approximately 27.8% of students who receive an allowance do not do chores.
In the "No Allowance" column, approximately 42.9% of students who do not receive an allowance do chores, while approximately 57.1% of students who do not receive an allowance do not do chores.

To find the relative frequencies of students in the survey by columns, we need to calculate the proportions of students within each column of the two-way table.

Column 1 represents students who receive an allowance, and Column 2 represents students who do not receive an allowance.

To calculate the relative frequencies of students in each column:

For the allowance column:
- Divide the frequency of students who do chores and receive an allowance (13) by the total number of students in the column (16).

Relative frequency of students who do chores and receive an allowance:
13/16 ≈ 0.8125

- Divide the frequency of students who do not do chores and receive an allowance (3) by the total number of students in the column (16).

Relative frequency of students who do not do chores and receive an allowance:
3/16 ≈ 0.1875

For the no allowance column:
- Divide the frequency of students who do chores and do not receive an allowance (5) by the total number of students in the column (9).

Relative frequency of students who do chores and do not receive an allowance:
5/9 ≈ 0.5556

- Divide the frequency of students who do not do chores and do not receive an allowance (4) by the total number of students in the column (9).

Relative frequency of students who do not do chores and do not receive an allowance:
4/9 ≈ 0.4444

Now, let's interpret the relative frequencies:

In the allowance column, approximately 81.25% (0.8125) of the students who receive an allowance do chores, while around 18.75% (0.1875) of the students who receive an allowance do not do chores.

In the no allowance column, approximately 55.56% (0.5556) of the students who do not receive an allowance do chores, while around 44.44% (0.4444) of the students who do not receive an allowance do not do chores.

These relative frequencies provide insights into the relationship between receiving an allowance and doing chores at home among the surveyed students.