Grade 6 math worksheet on statistics and probability, focusing on creating frequency tables and histograms from numerical data.

Let's solve this step-by-step based on the image you've provided.

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Task Overview

We are given a list of History final exam test scores, and we need to:
1. Create a frequency table by grouping the scores into intervals.
2. Use that data to draw a histogram.

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Step 1: List of Test Scores

Here are the test scores:

```
94, 82, 82, 63, 98, 78, 69,
54, 51, 98, 72, 80, 90, 77,
76, 80, 80, 91, 78, 41, 69,
65, 43, 65, 75, 43, 93, 59
```

Let’s count how many scores fall into each interval.

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Step 2: Define Intervals and Count Frequencies

The intervals are already given in the frequency table:

| Test Scores | Frequency |
|-------------|-----------|
| 41 - 50 | |
| 51 - 60 | |
| 61 - 70 | |
| 71 - 80 | |
| 81 - 90 | |
| 91 - 100 | |

Now, let's go through each score and count how many fall into each range.

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#### Counting:

41 - 50:
- 41, 43, 43 → That’s 3 scores

✔ 41, 43, 43 → 3 values

51 - 60:
- 54, 51, 59 → That’s 3 scores

✔ 51, 54, 59 → 3 values

61 - 70:
- 63, 69, 69, 65, 65 → That’s 5 scores

✔ 63, 65, 65, 69, 69 → 5 values

71 - 80:
- 78, 72, 77, 76, 78, 75 → That’s 6 scores

✔ 72, 75, 76, 77, 78, 78 → 6 values

81 - 90:
- 82, 82, 80, 80, 80, 80, 80? Wait — let's check carefully:

Wait! 80 is not in 81–90. It's in 71–80.

So which scores are between 81 and 90?

- 82, 82, 80 (no), 80 (no), 80 (no), 80 (no) → only 82, 82

But wait: 80 is below 81 → so not included.

So: 82, 82 → two scores?

Wait — look again:

From the list:
- 82, 82 → yes
- 80 → no (it's in 71–80)
- 80 → no
- 80 → no
- 80 → no
- 80 → no

Also: 80 appears three times? Let's list all:

Scores:
- 82, 82 → 81–90 ✔
- 80 → 71–80 ✘
- 80 → 71–80 ✘
- 80 → 71–80 ✘
- 80 → 71–80 ✘
- 80 → 71–80 ✘

Wait — actually, there are four 80s?

Let me recount the full list:

Original list:
```
94, 82, 82, 63, 98, 78, 69,
54, 51, 98, 72, 80, 90, 77,
76, 80, 80, 91, 78, 41, 69,
65, 43, 65, 75, 43, 93, 59
```

Now extract scores in 81–90:

- 82, 82 → yes
- 80 → no (≤80)
- 80 → no
- 80 → no
- 80 → no
- 90 → yes (90 is ≤90 and ≥81) → yes
- 91 → no (≥91)

So:
- 82, 82 → 2
- 90 → 1

So total: 3 scores in 81–90

✔ 82, 82, 90 → 3 values

91 - 100:
- 94, 98, 98, 91, 93 → let's check:

- 94 → yes
- 98 → yes
- 98 → yes
- 91 → yes
- 93 → yes

So: 94, 98, 98, 91, 93 → 5 scores

✔ 5 values

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Final Frequency Table

| Test Scores | Frequency |
|-------------|-----------|
| 41 - 50 | 3 |
| 51 - 60 | 3 |
| 61 - 70 | 5 |
| 71 - 80 | 6 |
| 81 - 90 | 3 |
| 91 - 100 | 5 |

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Step 3: Histogram

To draw the histogram:

- X-axis: Test Score Ranges (41–50, 51–60, ..., 91–100)
- Y-axis: Frequency (number of students)

Each bar will have:
- Width: equal for each interval
- Height: corresponding frequency

So the bars should be:
- 41–50: height 3
- 51–60: height 3
- 61–70: height 5
- 71–80: height 6
- 81–90: height 3
- 91–100: height 5

Make sure the bars touch each other (since it's continuous data).

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✔ Final Answer:

#### Frequency Table

| Test Scores | Frequency |
|-------------|-----------|
| 41 - 50 | 3 |
| 51 - 60 | 3 |
| 61 - 70 | 5 |
| 71 - 80 | 6 |
| 81 - 90 | 3 |
| 91 - 100 | 5 |

#### Histogram Instructions
Draw bars with:
- X-axis labeled with intervals: 41–50, 51–60, ..., 91–100
- Y-axis from 0 to 7 (since max frequency is 6)
- Heights: 3, 3, 5, 6, 3, 5 respectively
- Bars adjacent to each other (no gaps)

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📊 Summary

This frequency table and histogram show how test scores are distributed across different ranges. The most common scores were in the 71–80 range (6 students), followed by 61–70 and 91–100 (5 each). The lowest frequencies were in the 41–50 and 51–60 ranges (3 each).

You can now fill in the table and sketch the histogram accordingly!

Let me know if you'd like a visual sketch or help drawing it!