Question

# A Washerman asks 75 people from two different cities if they own rain boots. Complete thetwo-way frequency table to show the results of the survey.

What pattern do you see in the two-way frequency table?

Hint:

- Categories are labelled in the left column and top row.
- The counts are placed in the centre of the table.
- Totals appear at the end of each row and column.
- A sum of all counts (a grand total) is placed at the bottom right

## The correct answer is: 32,43,75

### Answer:

Given:

Yes

No

Total

City A

a

19

32

City B

28

b

d

Total

c

34

e

- Step 1:

Find a.

As, we know,

Totals appear at the end of each row and column

a + 19 = 32

a = 32 – 19

a = 13

- Step 2:

Find c.

As, we know,

Totals appear at the end of each row and column

a + 28 = c

c = 28 + 13

c = 41

- Step 3:

Find b.

As, we know,

Totals appear at the end of each row and column

b + 19 = 34

b = 34 – 19

b = 15

- Step 4:

Find d

As, we know,

Totals appear at the end of each row and column

28 + b = d

d = 28 + 15

d = 43

- Step 5:

Find e.

As, we know,

A sum of all counts (a grand total) is placed at the bottom right

32 + d = e

e = 32 + 43

e = 75

- Final Answer:

Yes

No

Total

City A

13

19

32

City B

28

15

43

Total

41

34

75

Yes

No

Total

City A

a

19

32

City B

28

b

d

Total

c

34

e

Yes

No

Total

City A

13

19

32

City B

28

15

43

Total

41

34

75

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