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This worksheet is asking to compare two students' (Lin and Clare) abilities to estimate the mass of objects, with some statistical summaries provided. Both students were trying to estimate the mass of eight different objects that actually weigh 2,000 grams each. The key statistics given are:

- **Lin:**
  - Mean: 2,000 grams
  - MAD (Mean Absolute Deviation): 225 grams
  - Median: 1,950 grams
  - IQR (Interquartile Range): 350 grams

- **Clare:**
  - Mean: 2,000 grams
  - MAD: 275 grams
  - Median: 2,000 grams
  - IQR: 500 grams

### Comparison:
1. **Mean**: Both Lin and Clare have a mean of 2,000 grams, which matches the actual weight of the objects. This indicates that, on average, both students’ estimates were correct.
  
2. **MAD (Mean Absolute Deviation)**: Lin's MAD is 225 grams, while Clare's is 275 grams. The MAD represents the average distance of each estimate from the mean. Lin's MAD is smaller, meaning Lin's estimates were, on average, closer to the mean than Clare's.

3. **Median**: Lin's median estimate is 1,950 grams, while Clare's is 2,000 grams. Clare's median exactly matches the actual value, whereas Lin's is slightly lower, which suggests Clare's estimates were more centered around the true value.

4. **IQR (Interquartile Range)**: Lin's IQR is 350 grams, while Clare's is 500 grams. The IQR measures the spread of the middle 50% of the estimates. A smaller IQR indicates that the estimates were more tightly clustered around the median. Lin's IQR is smaller, indicating less variability in Lin's middle estimates compared to Clare's.

### Conclusion:
Although both students have the same mean, Lin's estimates are slightly more consistent (lower MAD and IQR), meaning they are less spread out and generally closer to the true value. Clare has a more accurate median (exactly 2,000 grams), but her estimates show more variability. Based on the lower MAD and IQR, **Lin** seems to be slightly better at estimating the mass of the objects.

Would you like more details on any part of this analysis? Here are five related questions:

1. What does it mean if the mean is equal to the actual value but the MAD is high?
2. How does the median help us understand the spread of data compared to the mean?
3. Why is a lower IQR considered beneficial in this comparison?
4. How would the result change if the MAD were equal for both students?
5. Could Clare's exact median be more important than Lin's lower MAD? Why?

**Tip**: The **MAD** is a helpful measure of variability, but it should always be considered alongside other statistics like the mean and median for a complete picture.

In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams. Summary statistics are provided for both students, including mean, MAD, median, and IQR. The task is to determine which student was better at estimating the mass of the objects and explain the reasoning.

Explore how Lin and Clare's ability to estimate the mass of objects is analyzed through descriptive statistics. The summary includes mean, median, MAD, and IQR, helping to understand who made more accurate estimates. Suitable for middle school students learning about variability and data analysis.

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