Worksheet on relative frequency tables with exercises to calculate missing relative frequencies for different data categories.

Let's solve the problem step by step.

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Part 1: The Missing Relative Frequencies

We need to calculate missing relative frequencies for two tables.

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#### Table 1: Car Brands Owned

| Car Brands Owned | Number | Rel. Fre. |
|------------------|--------|----------|
| Nissan | 18 | 0.257 |
| Toyota | 12 | ? |
| Honda | 20 | 0.285 |
| Kia | 7 | 0.1 |
| Ford | 13 | ? |
| Total | 70 | |

> Relative Frequency (Rel. Fre.) = (Number) / (Total)

Let’s find missing values:

- Toyota:
$ \frac{12}{70} = 0.1714 $ → Rounded to 0.171

- Ford:
$ \frac{13}{70} = 0.1857 $ → Rounded to 0.186

✔ Let’s verify:
- Nissan: $ 18/70 = 0.257 $ ✔
- Honda: $ 20/70 ≈ 0.2857 $ → Given as 0.285 ✔ (rounded)
- Kia: $ 7/70 = 0.1 $ ✔
- Total: $ 18+12+20+7+13 = 70 $ ✔

So, completed table:

| Car Brands Owned | Number | Rel. Fre. |
|------------------|--------|----------|
| Nissan | 18 | 0.257 |
| Toyota | 12 | 0.171 |
| Honda | 20 | 0.285 |
| Kia | 7 | 0.1 |
| Ford | 13 | 0.186 |
| Total | 70 | |

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#### Table 2: Favourite Seasons

| Favourite Seasons | Number | Rel. Fre. |
|-------------------|--------|----------|
| Spring | 20 | ? |
| Summer | 15 | 0.194 |
| Fall | 23 | ? |
| Winter | 13 | 0.168 |
| None | 6 | 0.08 |
| Total | 77 | |

Check total: $ 20 + 15 + 23 + 13 + 6 = 77 $ ✔

Now compute missing relative frequencies:

- Spring:
$ \frac{20}{77} ≈ 0.2597 $ → Rounded to 0.260

- Fall:
$ \frac{23}{77} ≈ 0.2987 $ → Rounded to 0.299

Check given ones:
- Summer: $ 15/77 ≈ 0.1948 $ → Given as 0.194 ✔
- Winter: $ 13/77 ≈ 0.1688 $ → Given as 0.168 ✔
- None: $ 6/77 ≈ 0.0779 $ → Given as 0.08 → Close but not exact. Wait — let's check:

Wait! $ 6/77 ≈ 0.0779 $, but it's given as 0.08, which is rounded.

But if we use 0.08, then total of rel. freqs should be 1.

Let’s sum up known and calculated:

- Spring: 0.260
- Summer: 0.194
- Fall: 0.299
- Winter: 0.168
- None: 0.08

Sum: $ 0.260 + 0.194 + 0.299 + 0.168 + 0.08 = 1.001 $ → Very close to 1, acceptable due to rounding.

So, final values:

| Favourite Seasons | Number | Rel. Fre. |
|-------------------|--------|----------|
| Spring | 20 | 0.260 |
| Summer | 15 | 0.194 |
| Fall | 23 | 0.299 |
| Winter | 13 | 0.168 |
| None | 6 | 0.08 |
| Total | 77 | |

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Think About It:

> When looking at a relative frequency chart, before calculating the relative frequencies, can we tell which numbers or categories will have the highest relative frequency?

✔ Yes, because the category with the highest number (frequency) will have the highest relative frequency, assuming the total is constant.

So, just by comparing the counts, we can predict which one has the highest relative frequency.

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Part 2: Calculating Relative Frequencies

#### Table 3: Sandwiches Sold

| Sandwiches Sold | Number | Rel. Fre. |
|------------------|--------|----------|
| Monday | 30 | ? |
| Tuesday | 18 | ? |
| Wednesday | 22 | ? |
| Thursday | 15 | ? |
| Friday | 25 | ? |
| Total | ? | |

First, calculate total:
$ 30 + 18 + 22 + 15 + 25 = 110 $

Now calculate each relative frequency:

- Monday: $ \frac{30}{110} ≈ 0.2727 $ → 0.273
- Tuesday: $ \frac{18}{110} ≈ 0.1636 $ → 0.164
- Wednesday: $ \frac{22}{110} = 0.2 $ → 0.200
- Thursday: $ \frac{15}{110} ≈ 0.1364 $ → 0.136
- Friday: $ \frac{25}{110} ≈ 0.2273 $ → 0.227

Check total:
$ 0.273 + 0.164 + 0.200 + 0.136 + 0.227 = 1.000 $ ✔

Final Table:

| Sandwiches Sold | Number | Rel. Fre. |
|------------------|--------|----------|
| Monday | 30 | 0.273 |
| Tuesday | 18 | 0.164 |
| Wednesday | 22 | 0.200 |
| Thursday | 15 | 0.136 |
| Friday | 25 | 0.227 |
| Total | 110| |

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#### Table 4: Heights of Friends

| Heights of Friends | Number | Rel. Fre. |
|--------------------|--------|----------|
| 160 cm | 8 | ? |
| 165 cm | 4 | ? |
| 170 cm | 6 | ? |
| 175 cm | 2 | ? |
| 180 cm | 5 | ? |
| Total | ? | |

Total: $ 8 + 4 + 6 + 2 + 5 = 25 $

Now compute relative frequencies:

- 160 cm: $ \frac{8}{25} = 0.32 $
- 165 cm: $ \frac{4}{25} = 0.16 $
- 170 cm: $ \frac{6}{25} = 0.24 $
- 175 cm: $ \frac{2}{25} = 0.08 $
- 180 cm: $ \frac{5}{25} = 0.20 $

Total: $ 0.32 + 0.16 + 0.24 + 0.08 + 0.20 = 1.00 $ ✔

Final Table:

| Heights of Friends | Number | Rel. Fre. |
|--------------------|--------|----------|
| 160 cm | 8 | 0.32 |
| 165 cm | 4 | 0.16 |
| 170 cm | 6 | 0.24 |
| 175 cm | 2 | 0.08 |
| 180 cm | 5 | 0.20 |
| Total | 25 | |

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✔ Final Answers Summary:

#### Car Brands Owned:
- Toyota: 0.171
- Ford: 0.186

#### Favourite Seasons:
- Spring: 0.260
- Fall: 0.299

#### Sandwiches Sold:
- Monday: 0.273
- Tuesday: 0.164
- Wednesday: 0.200
- Thursday: 0.136
- Friday: 0.227
- Total: 110

#### Heights of Friends:
- 160 cm: 0.32
- 165 cm: 0.16
- 170 cm: 0.24
- 175 cm: 0.08
- 180 cm: 0.20
- Total: 25

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Think About It Answer:

Yes, we can tell that the category with the highest number will have the highest relative frequency, since relative frequency is proportional to the count when the total is fixed.

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