Question

1. during the month of august, the mean of the daily rainfall in one city was 0.04 inches with a standard deviation of 0.15 inches. in another city, the mean of the daily rainfall was 0.01 inches with a standard deviation of 0.05 inches. han says that both cities had a similar pattern of precipitation in the month of august. do you agree with han? explain your reasoning.

Explanation:

Step1: Recall the concept of standard deviation

Standard deviation measures the spread of data. A smaller standard deviation means data is more clustered around the mean, a larger one means more spread out.

Step2: Compare the standard deviations

One city has a standard deviation of \(0.05\) inches and the other has \(0.15\) inches. Since \(0.05
eq0.15\), the spreads (patterns) of daily rainfall are different.

Answer:

No, I do not agree with Han. The standard deviations of the two cities' daily rainfall (\(0.05\) inches and \(0.15\) inches) are different. A smaller standard deviation (\(0.05\)) implies that the daily rainfall in one city is more clustered around its mean (\(0.01\) inches), while a larger standard deviation (\(0.15\)) for the other city means its daily rainfall is more spread out around its mean (\(0.04\) inches). So, they do not have a similar pattern of precipitation.