Question

the values for three different sets of data are shown.

data set	data points
2	22, 78, 84, 88, 92
3	0, 1, 3, 6

without calculating any statistics, gabriel knew that data set 3 would have the lowest mean absolute deviation among the three sets. how does he know?

• because set 3 has the lowest mean.
• because set 3 had the least amount of data points.
• because set 1 and set 2 contain outliers.
• because set 1 and set 2 have an odd number of data points.

Explanation:

• Analyze Option 1: Mean absolute deviation (MAD) is about data spread, not mean value. So Set 3 having the lowest mean doesn't imply lowest MAD. Eliminate this.
• Analyze Option 2: MAD depends on data spread, not number of data points. Set 3 has 4 points, but that's not why MAD is low. Eliminate this.
• Analyze Option 3: Outliers increase data spread (and MAD). Set 1 has 96 (outlier), Set 2 has 22 (outlier). Set 3 has no outliers, so data is more clustered, leading to lower MAD. This makes sense.
• Analyze Option 4: Number of data points being odd/even doesn't affect MAD. MAD depends on spread, not parity of data points count. Eliminate this.

Answer:

Because Set 1 and Set 2 contain outliers.