Two Way Frequency Table Worksheet | Download Free PDF | Minimum ... - Free Printable

Let’s solve each part step by step.

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Problem 1: Snowboards and Skateboards Table

Table given:

| | Likes Skateboards | Do not like Skateboards | Total |
|---------------------|-------------------|--------------------------|-------|
| Likes Snowboards | 15 | 12 | 27 |
| Do not like Snowboards | 23 | 18 | 41 |
| Total | 38 | 30 | 68|

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a. How many students participated in the survey?

Look at the bottom-right corner of the table — that’s the grand total.

→ 68 students

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b. How many students said they like snowboards? What type of frequency is this?

Look at the “Likes Snowboards” row → total is 27.

This is a marginal frequency — it’s the total for one category (likes snowboards), regardless of the other variable.

→ 27 students; marginal frequency

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c. How many students like snowboards, but do not like skateboards? What type of frequency is this?

Look at the cell where “Likes Snowboards” row meets “Do not like Skateboards” column → 12

This is a joint frequency — it counts people who fall into both categories at once.

→ 12 students; joint frequency

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Problem 2: Minimum Wage Survey Table

Given incomplete table:

| | For | Against | No Opinion | TOTAL |
|---------------|-----|---------|------------|-------|
| Ages 21-40 | ? | 20 | 5 | 50 |
| Ages 41-60 | 30 | ? | 15 | ? |
| Over 60 | 50 | 20 | ? | 75 |
| TOTAL | ? | 70 | 25 | 200 |

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a. Fill in the missing data

We’ll fill row by row and column by column using totals.

Start with Ages 21-40:

Total = 50
Against = 20, No Opinion = 5
So For = 50 - 20 - 5 = 25

→ Ages 21-40, For = 25

Now Over 60:

Total = 75
For = 50, Against = 20
No Opinion = 75 - 50 - 20 = 5

→ Over 60, No Opinion = 5

Now Ages 41-60:

We know For = 30, No Opinion = 15
But we don’t know Against or Total yet.

Use column totals.

Column “Against” total = 70
We have:
Ages 21-40: 20
Over 60: 20
So Ages 41-60 Against = 70 - 20 - 20 = 30

Then Ages 41-60 Total = 30 (For) + 30 (Against) + 15 (No Opinion) = 75

Now check row totals:

Ages 21-40: 25+20+5=50 ✔
Ages 41-60: 30+30+15=75 ✔
Over 60: 50+20+5=75 ✔
Grand total: 50+75+75=200 ✔

Now column “For” total:

Ages 21-40: 25
Ages 41-60: 30
Over 60: 50
Total For = 25+30+50 = 105

Check column “No Opinion”: 5+15+5=25 ✔

Final filled table:

| | For | Against | No Opinion | TOTAL |
|---------------|-----|---------|------------|-------|
| Ages 21-40 | 25 | 20 | 5 | 50 |
| Ages 41-60 | 30 | 30 | 15 | 75 |
| Over 60 | 50 | 20 | 5 | 75 |
| TOTAL | 105 | 70 | 25 | 200 |

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b. Create a two-way relative frequency table

Relative frequency = each cell value ÷ grand total (200)

We’ll calculate each cell as decimal or percent? The problem doesn’t specify, but since later questions ask for percentages, let’s use decimals rounded to 3 places or fractions. But usually in school, they want decimals or percents. Let’s do decimals to 3 places.

Actually, let’s do it as proportions (decimals) unless asked for percent.

But looking ahead, parts c-g ask for percentages, so maybe better to compute as decimals and then convert when needed.

But for the table, let’s write as decimals rounded to 3 places.

Compute each:

Ages 21-40:
- For: 25/200 = 0.125
- Against: 20/200 = 0.100
- No Opinion: 5/200 = 0.025
- Total: 50/200 = 0.250

Ages 41-60:
- For: 30/200 = 0.150
- Against: 30/200 = 0.150
- No Opinion: 15/200 = 0.075
- Total: 75/200 = 0.375

Over 60:
- For: 50/200 = 0.250
- Against: 20/200 = 0.100
- No Opinion: 5/200 = 0.025
- Total: 75/200 = 0.375

Totals:
- For: 105/200 = 0.525
- Against: 70/200 = 0.350
- No Opinion: 25/200 = 0.125
- Grand Total: 200/200 = 1.000

So relative frequency table:

| | For | Against | No Opinion | TOTAL |
|---------------|---------|---------|------------|---------|
| Ages 21-40 | 0.125 | 0.100 | 0.025 | 0.250 |
| Ages 41-60 | 0.150 | 0.150 | 0.075 | 0.375 |
| Over 60 | 0.250 | 0.100 | 0.025 | 0.375 |
| TOTAL | 0.525 | 0.350 | 0.125 | 1.000 |

(You could also write as percentages: multiply by 100 → 12.5%, etc., but since the question says “relative frequency”, decimals are fine.)

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Now answer the questions using the tables.

c. Out of the people that have no opinion, what percentage is over 60 years old?

People with no opinion = 25 (from total row)

Of those, over 60 = 5

Percentage = (5 / 25) × 100 = 20%

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d. What percentage of people want to increase minimum wage?

Want to increase = “For” total = 105

Total people = 200

Percentage = (105 / 200) × 100 = 52.5%

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e. How many people over 60 are against increasing the minimum wage?

From table: Over 60, Against = 20

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f. For ages 21-60 how many were for increasing the minimum wage?

Ages 21-60 means Ages 21-40 AND Ages 41-60

For 21-40: 25
For 41-60: 30
Total = 25 + 30 = 55

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g. What percent of people over 60 are against or have no opinion?

Over 60 total = 75

Against = 20
No Opinion = 5
Sum = 25

Percent = (25 / 75) × 100 = 33.33...% ≈ 33.3%

(Or exactly 1/3, but usually round to one decimal place.)

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✔ All calculations checked.

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Final Answer:

Problem 1:

a. 68
b. 27; marginal frequency
c. 12; joint frequency

Problem 2:

a. Filled table:

| | For | Against | No Opinion | TOTAL |
|---------------|-----|---------|------------|-------|
| Ages 21-40 | 25 | 20 | 5 | 50 |
| Ages 41-60 | 30 | 30 | 15 | 75 |
| Over 60 | 50 | 20 | 5 | 75 |
| TOTAL | 105 | 70 | 25 | 200 |

b. Relative frequency table (as decimals):

| | For | Against | No Opinion | TOTAL |
|---------------|---------|---------|------------|---------|
| Ages 21-40 | 0.125 | 0.100 | 0.025 | 0.250 |
| Ages 41-60 | 0.150 | 0.150 | 0.075 | 0.375 |
| Over 60 | 0.250 | 0.100 | 0.025 | 0.375 |
| TOTAL | 0.525 | 0.350 | 0.125 | 1.000 |

c. 20%
d. 52.5%
e. 20
f. 55
g. 33.3%