https://file.aiquickdraw.com/mathbot/file/17255435992329hp3p5ir.jpg

Let's address each part of the problem as per the image:

**a) Explain why this is not a good way to record the results.**

The table shows pairs of numbers from two dice throws, with the sums recorded in each cell. This isn't ideal because it only records the sums of the dice, not the actual values of each dice throw. As a result, we lose information about individual die results, making it impossible to distinguish between different combinations that could produce the same sum (e.g., a sum of 7 can come from (1,6), (2,5), (3,4), etc.).

**b) Show the frequencies for each number in a suitable table.**

Let's list the sums from the table and count their frequencies:

| Sum | Frequency |
|-----|-----------|
| 2   | 3         |
| 3   | 5         |
| 4   | 7         |
| 5   | 10        |
| 6   | 10        |
| 7   | 14        |
| 8   | 9         |
| 9   | 12        |
| 10  | 13        |
| 11  | 11        |
| 12  | 6         |

**c) Show the results in a bar chart.**

Here is a description of how you could draw the bar chart:

- The x-axis should represent the sums (from 2 to 12).
- The y-axis should represent the frequency of each sum.
- Each bar's height should correspond to the frequency of the sum.

**d) Is Sofia’s prediction correct? Give a reason for your answer.**

Without Sofia’s prediction statement, it is difficult to provide an exact answer. If her prediction was that the frequency of sums closer to 7 would be higher, then she is correct because the frequencies around 7 (6, 7, 8) are indeed higher than others.

**e) Is Zara’s prediction correct? Give a reason for your answer.**

Similarly, Zara’s prediction is not provided in the image. If Zara predicted that certain sums, like 2 or 12, would be less frequent, she would be correct as the sums of 2 and 12 occur the least.

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Do you want any more details or have specific questions? Here are some related questions:

1. How do the frequencies of dice sums compare to the expected probabilities?
2. Why is the sum of 7 the most frequent in dice rolls?
3. How could the recording method be improved for better analysis?
4. What other patterns might emerge from recording individual dice results?
5. How could you use this data to explore probability and statistics concepts?

**Tip:** When analyzing dice rolls, remember that each sum has different probabilities due to the number of combinations that produce it.

They throw the two dice 100 times. Their results are shown in the table. Explain why this is not a good way to record the results. Show the frequencies for each number in a suitable table. Show the results in a bar chart. Is Sofia’s prediction correct? Give a reason for your answer. Is Zara’s prediction correct? Give a reason for your answer.

Explore how to analyze and record dice rolls using frequency distribution and bar charts. Understand why recording the sum of dice rolls is not ideal and learn how to verify predictions using statistical concepts. Suitable for students in Grades 6-8.

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