Question

1 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?
explain your reasoning.

Explanation:

To determine who estimated better, we analyze measures of center (mean, median) and spread (MAD, IQR). Both have a mean of 2000 (matches actual mass). For spread, a smaller MAD and IQR mean estimates are closer to the actual value. Lin has a smaller MAD (225 vs. 275) and smaller IQR (350 vs. 500), so Lin's estimates are more consistent and closer to 2000 grams.

Answer:

Lin was better at estimating the mass of the objects. Both Clare and Lin have a mean estimate of 2,000 grams (matching the actual mass). However, Lin has a smaller Mean Absolute Deviation (MAD = 225 grams vs. Clare’s MAD = 275 grams) and a smaller Interquartile Range (IQR = 350 grams vs. Clare’s IQR = 500 grams). Smaller MAD and IQR indicate that Lin’s estimates are more consistent and closer to the actual mass of 2,000 grams on average, showing less variability in her estimates.