Question

two months ago, the mean daily rainfall in a local city was 9.4 cm. the mean absolute deviation was 3.5 cm. last month, the mean daily rainfall in that city was 11.5 cm, and the mean absolute deviation was 1.6 cm. which statement about the rainfall is true? about the same amount of rain fell two months ago as last month. last month, the amount of rain that fell each day varied less than the month before. last month, the amount of rain that fell each day varied about the same as the month before. more rain fell two months ago than last month.

Explanation:

Step1: Understand the meaning of mean absolute deviation

The mean absolute deviation (MAD) measures the average distance between each data point and the mean. A smaller MAD indicates that the data points are closer to the mean (less variation), and a larger MAD indicates that the data points are more spread out (more variation).

Step2: Compare the MAD values

Two months ago, the MAD was \(3.5\) cm. Last month, the MAD was \(1.6\) cm. Since \(1.6<3.5\), the amount of rain that fell each day last month varied less than the month before (two months ago).

Step3: Analyze the mean values

The mean two months ago was \(9.4\) cm and last month it was \(11.5\) cm. So, more rain fell last month than two months ago.

Answer:

Last month, the amount of rain that fell each day varied less than the month before.