In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each.

Some summary statistics:

Clare

mean: 2,000 grams
MAD: 275 grams
median: 2,000 grams
IQR: 500 grams
Lin

mean: 2,000 grams
MAD: 225 grams
median: 1,950 grams
IQR: 350 grams
Which student was better at estimating the mass of the objects?

To determine which student was better at estimating the mass of the objects, let's evaluate the **accuracy** and **consistency** of their estimates using the summary statistics provided.

### Clare's Statistics:
- **Mean**: 2,000 grams (matches the actual mass, indicating accuracy).
- **MAD (Mean Absolute Deviation)**: 275 grams (indicates how far the estimates deviate, on average, from the mean).
- **Median**: 2,000 grams (matches the actual mass, reinforcing accuracy).
- **IQR (Interquartile Range)**: 500 grams (measures the spread of the middle 50% of estimates, indicating variability).

### Lin's Statistics:
- **Mean**: 2,000 grams (matches the actual mass, indicating accuracy).
- **MAD**: 225 grams (indicates smaller deviations on average compared to Clare's, suggesting Lin's estimates are more consistent).
- **Median**: 1,950 grams (slightly less accurate, as it's 50 grams lower than the actual mass).
- **IQR**: 350 grams (indicates less variability in the estimates compared to Clare's).

### Conclusion:
- **Accuracy**: Both students have the same **mean** of 2,000 grams, which matches the actual mass. However, Lin's **median** of 1,950 grams is slightly lower than Clare's, which is exactly 2,000 grams. In this regard, Clare has a slight edge in accuracy.
  
- **Consistency**: Lin has a lower **MAD** (225 grams vs. Clare's 275 grams) and a smaller **IQR** (350 grams vs. Clare's 500 grams), which means Lin's estimates were more consistent and had less variability.

### Final Judgment:
Lin was more **consistent** in their estimates (lower MAD and IQR), but Clare's estimates were slightly more **accurate** (exact median of 2,000 grams). If we prioritize consistency (since both had a mean of 2,000 grams), **Lin** might be considered the better estimator overall, despite the slightly lower median.

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Would you like more details on these metrics or have any questions?

Here are 5 related questions:
1. What is the significance of the MAD in measuring consistency?
2. How does the IQR help in understanding the spread of data?
3. In what scenarios would we prioritize accuracy over consistency?
4. How could Lin improve their accuracy in this experiment?
5. How is the mean affected by extreme values or outliers?

**Tip**: When evaluating data, always check both accuracy (mean and median) and consistency (MAD and IQR) for a full picture.

In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each. Clare's mean: 2,000 grams, MAD: 275 grams, median: 2,000 grams, IQR: 500 grams. Lin's mean: 2,000 grams, MAD: 225 grams, median: 1,950 grams, IQR: 350 grams. Which student was better at estimating the mass of the objects?

In this problem, Clare and Lin estimate the mass of objects weighing 2,000 grams. We compare their accuracy using mean, MAD, median, and IQR. Learn how Clare's and Lin's estimates differ in consistency and accuracy, making it suitable for Grades 6-8.

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