Question

the values for three sets of data are shown below.

data set	values
2	63, 29, 35, 28, 30
3	2, 5, 3, 8

without calculating any statistics, anna knows that data set 3 would have the least mean absolute deviation among the three sets. which statement explains how she knows?

• sets 1 and 2 contain outliers.
• set 3 has the least mean.
• set 3 contains an outlier.
• sets 1 and 2 have an odd number of values.

Explanation:

To determine why Data Set 3 has the least mean absolute deviation (MAD), we analyze each option:

• Option 1 (Sets 1 and 2 contain outliers): Data Set 1 has 88 (an outlier, far from other values: 42, 48, 49, 50). Data Set 2 has 63 (an outlier, far from 28, 29, 30, 35). Outliers increase MAD by creating large deviations from the mean. Data Set 3 has values (2, 3, 5, 8) that are close together, so no extreme outliers, leading to smaller MAD. This matches Anna’s reasoning.
• Option 2 (Set 3 has the least mean): MAD depends on deviation from the mean, not the mean’s size. A small mean doesn’t guarantee small MAD (e.g., a set with values 1, 100 would have a low mean but high MAD). Eliminate.
• Option 3 (Set 3 contains an outlier): Set 3’s values (2, 3, 5, 8) are all relatively close; no outlier exists. Eliminate.
• Option 4 (Sets 1 and 2 have an odd number of values): The number of values (odd/even) doesn’t affect MAD. MAD depends on data spread, not count parity. Eliminate.

Answer:

A. Sets 1 and 2 contain outliers.