Question

the annual rainfall for austin, texas, and san antonio, texas, in each of the years from 2002 to 2011 are shown in the tables. use the data for 9–11. annual rainfall for austin, texas (in.) 36.0021.4152.2722.3334.7046.9516.0731.3837.7619.68 annual rainfall for san antonio, texas (in.) 46.2728.4545.3216.5421.3447.2513.7630.6937.3917.58. use the mads to compare the distribution of annual rainfall in the two cities

Answer 1

The Mean Absolute Deviation (MAD) for annual rainfall in Austin is 8.693, indicating less variability around the mean, while in San Antonio, it is 10.097, suggesting greater variability.

Let's calculate the Mean Absolute Deviation (MAD) for the annual rainfall data in Austin and San Antonio.

1. Calculate the Mean:

- Austin Mean: Austin Mean = (36.00 + 21.41 + 52.27 + ...
+ 19.68) / 10 = 28.273

- San Antonio Mean: San Antonio Mean} = (46.27 + 28.45 + 45.32 + ...
+ 17.58) / 10 = 29.463

2. Calculate Absolute Deviations:

- Austin Deviations:
`\(|36.00 - 28.273|, |21.41 - 28.273|, ..., |19.68 - 28.273|\`)

- San Antonio Deviations:
`\(|46.27 - 29.463|, |28.45 - 29.463|, ..., |17.58 - 29.463|\)`

3. Calculate MAD:

- Austin MAD:
`\(\text{Austin MAD} = (|36.00 - 28.273| + |21.41 - 28.273| + ... + |19.68 - 28.273|) / 10 = 8.693\)`

- San Antonio MAD:
`\(\text{San Antonio MAD} = (|46.27 - 29.463| + |28.45 - 29.463| + ... + |17.58 - 29.463|) / 10 = 10.097\)`

Comparing the MAD values, the Austin MAD of 8.693 is smaller than the San Antonio MAD of 10.097. This suggests that, on average, the annual rainfall values in Austin are less variable or more tightly clustered around the mean compared to San Antonio.