To determine which student was better at estimating the mass of the objects, we can evaluate their accuracy and variability based on the provided summary statistics.
1. Mean Accuracy:
- Both Clare and Lin have a mean estimate of 2,000 grams.
- Since both means are equal to the actual mass of the objects (2,000 grams), their mean estimates are equally accurate, and we cannot differentiate between the students based on mean accuracy.
2. Variability:
- Mean Absolute Deviation (MAD) is a measure of variability that indicates how spread out the estimates are around the mean.
- Clare's MAD is 275 grams, while Lin's MAD is 225 grams.
- Lin's MAD is lower than Clare's, indicating that Lin's estimates are less variable (i.e., more consistent or closer to the mean).
3. Median Comparison:
- Clare's median estimate is 2,000 grams, which matches the actual mass.
- Lin's median estimate is 1,950 grams, which is slightly lower than the actual mass.
- While Clare's median seems more accurate, using the median alone does not provide a full picture of the overall estimating ability.
4. Interquartile Range (IQR):
- Clare's IQR is 500 grams, whereas Lin's IQR is 350 grams.
- A lower IQR for Lin suggests that the middle 50% of her estimates are less spread out and more consistent compared to Clare's estimates.
Based on these analyses, we conclude that:
- Both Clare and Lin have equally accurate means.
- Lin exhibits less variability in her estimates compared to Clare, as indicated by both the lower MAD and lower IQR.
Thus, Lin was better at estimating the mass of the objects because Lin's responses were less variable.
