D-5: Do You Know How?
Grealize
INTEGRATED MATH I B - DUBOISE (LMS)
10-5: Do You Know How? (LMS graded)
S DO YOU KNOW HOW?
6. In a survey, customers select Item A or Item B. Item A is selected by 20
males and 10 females. Of 20 customers who select Item B, five are males.
Make a two-way relative frequency table to organize the data.
Previous
Item A
Male
20
Female
10
Totals
CHECK ANSWER
Item B
Total

To create a two-way relative frequency table, first, gather the total counts for each group based on gender and item selected:

Item A:
- Males: 20
- Females: 10

Item B:
- Males: 5
- Total: 20 (total number of people who chose Item B, both males and females)

Since we know that 5 males selected Item B, we can find the number of females who selected Item B:

Number of females who selected Item B = Total people who selected Item B - Males who selected Item B:
- Females: 20 - 5 = 15

Now we have our counts for both items:

Item A:
- Males: 20
- Females: 10

Item B:
- Males: 5
- Females: 15

Next, calculate the totals for each row (gender) and each column (item):

Total number of males = Males who selected Item A + Males who selected Item B:
- Males: 20 + 5 = 25

Total number of females = Females who selected Item A + Females who selected Item B:
- Females: 10 + 15 = 25

Total number of customers who selected Item A = Males who selected Item A + Females who selected Item A:
- Item A: 20 + 10 = 30

Total number of customers who selected Item B = Males who selected Item B + Females who selected Item B:
- Item B: 5 + 15 = 20

Grand total number of customers = Total males + Total females:
- Grand total: 25 + 25 = 50

Now, calculate the relative frequencies by dividing the count for each group by the grand total:

- Relative frequency of males selecting Item A = Males who selected Item A / Grand total
- Relative frequency of females selecting Item A = Females who selected Item A / Grand total
- Relative frequency of males selecting Item B = Males who selected Item B / Grand total
- Relative frequency of females selecting Item B = Females who selected Item B / Grand total
- Relative total frequency for males = Total males / Grand total
- Relative total frequency for females = Total females / Grand total
- Relative total frequency for Item A = Total Item A / Grand total
- Relative total frequency for Item B = Total Item B / Grand total

Here are the calculations:

- Relative frequency of males selecting Item A = 20 / 50 = 0.4
- Relative frequency of females selecting Item A = 10 / 50 = 0.2
- Relative frequency of males selecting Item B = 5 / 50 = 0.1
- Relative frequency of females selecting Item B = 15 / 50 = 0.3
- Relative total frequency for males = 25 / 50 = 0.5
- Relative total frequency for females = 25 / 50 = 0.5
- Relative total frequency for Item A = 30 / 50 = 0.6
- Relative total frequency for Item B = 20 / 50 = 0.4

Finally, construct the two-way relative frequency table:

| | Item A | Item B | Total |
|----------|--------|--------|-------|
| Male | 0.4 | 0.1 | 0.5 |
| Female | 0.2 | 0.3 | 0.5 |
| Total | 0.6 | 0.4 | 1 |

Each cell in the table gives the relative frequency of the customers based on their selection of Item A or Item B and their gender. The final row and column provide the total relative frequency for each row and column respectively.