Frequency Table Worksheet - Twinkl - Free Printable

Let's solve this step by step based on the worksheet.

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Step 1: Understand What Frequency Means

What is frequency?
Frequency refers to how often a particular value or category appears in a data set. In this case, it’s how many times each shoe size appears among Mr. Scott’s students.

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Step 2: List the Data

The shoe sizes are:

7, 9, 5, 6, 8, 10, 7, 5, 11, 8, 9, 6, 7, 9, 7, 6, 7, and 11

Let’s count how many values there are total:
- Count: 18 students

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Step 3: Create the Frequency Table

We’ll go through each shoe size and tally how many times it appears.

| Shoe Size | Tally | Frequency |
|-----------|---------------|-----------|
| 5 | || | 2 |
| 6 | ||| | 3 |
| 7 | |||| | | 5 |
| 8 | || | 2 |
| 9 | ||| | 3 |
| 10 | | | 1 |
| 11 | || | 2 |

> Explanation of Tally Marks:
> - Each “|” is one occurrence.
> - Every fifth mark is drawn diagonally across the previous four (like a group of 5).
> - So for 7: "|||| |" = 5 + 1 = 6? Wait — let’s recount carefully.

Wait! Let’s double-check the counts.

Recounting the Data:

List:
7, 9, 5, 6, 8, 10, 7, 5, 11, 8, 9, 6, 7, 9, 7, 6, 7, 11

Now, count each:

- 5: appears at positions 3, 9 → 2 times
- 6: positions 4, 12, 16 → 3 times
- 7: positions 1, 7, 13, 15, 17 → 5 times
- 8: positions 5, 10 → 2 times
- 9: positions 2, 11, 14 → 3 times
- 10: position 6 → 1 time
- 11: positions 9, 18 → 2 times

✔ So our table is correct.

Now fill in the Tally column properly using tally marks.

| Shoe Size | Tally | Frequency |
|-----------|---------------|-----------|
| 5 | || | 2 |
| 6 | ||| | 3 |
| 7 | |||| | | 5 |
| 8 | || | 2 |
| 9 | ||| | 3 |
| 10 | | | 1 |
| 11 | || | 2 |

> Note: The tally for 7 should be five marks: `||||` with a diagonal line through them, but since we're typing, we write `|||| |` as shorthand.

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Answer the Questions

#### 1. What shoe size is most frequent?

- The highest frequency is 5, which corresponds to shoe size 7.
- ✔ Answer: 7

#### 2. What shoe size is least frequent?

- The lowest frequency is 1, which corresponds to shoe size 10.
- ✔ Answer: 10

#### 3. How many students wear a shoe size of 8 or above?

Shoe sizes ≥ 8: 8, 9, 10, 11

- 8 → 2
- 9 → 3
- 10 → 1
- 11 → 2

Total = 2 + 3 + 1 + 2 = 8 students

✔ Answer: 8

#### 4. What percentage of students wear a 7 or less?

Shoe sizes ≤ 7: 5, 6, 7

- 5 → 2
- 6 → 3
- 7 → 5

Total = 2 + 3 + 5 = 10 students

Total number of students = 18

Percentage = (10 / 18) × 100 ≈ 55.56%

✔ Answer: Approximately 55.56%

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✔ Final Answers:

1. Most frequent shoe size: 7
2. Least frequent shoe size: 10
3. Number wearing size 8 or above: 8
4. Percentage wearing size 7 or less: ≈ 55.56%

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✔ Completed Table:

| Shoe Size | Tally | Frequency |
|-----------|---------------|-----------|
| 5 | || | 2 |
| 6 | ||| | 3 |
| 7 | |||| | | 5 |
| 8 | || | 2 |
| 9 | ||| | 3 |
| 10 | | | 1 |
| 11 | || | 2 |

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