Question

a meteorologist is studying the monthly rainfall in a section of the brazilian rainforest. she recorded the monthly rainfall, in inches, for last year. they were:

10.4, 10.3, 11.7, 11.1, 8.0, 4.4, 2.6, 1.8, 2.5, 4.4, 7.3, 9.5

calculate the following for the data set:
mean:
median:
mode:
range:

which of the following is true if the data point 11.1 is corrected to 11.7?

• the mean increases.
• the median increases.
• the data set has two modes.
• the range increases.

if the next months rainfall is 23.1 inches, this will have the biggest effect on the dropdown

Explanation:

Analyze the effect of an extreme value

We are asked to determine which statistical measure is affected the most if a new data point of \(23.1\) inches is added to the existing monthly rainfall data set. We apply the Basic Statistics concepts of Measures of Center (mean, median) and Measures of Spread (range).

Compare the new data point to the existing data set

The existing data set consists of 12 values ranging from \(1.8\) to \(11.7\) inches:

$$ 1.8, 2.5, 2.6, 4.4, 4.4, 7.3, 8.0, 9.5, 10.3, 10.4, 11.1, 11.7 $$

The new data point is \(23.1\) inches, which is nearly double the maximum value of the current data set (\(11.7\) inches). This makes \(23.1\) an extreme outlier.

Evaluate the impact on each statistical measure

• Median: The median is a highly robust measure of center. Adding one data point shifts the median position by only half a step, resulting in a very small change.
• Mean: The mean is sensitive to outliers, but because it averages the sum over all \(13\) data points, the change is diluted.
• Range: The range is calculated as \(\text{Maximum} - \text{Minimum}\).
• Original range: \(11.7 - 1.8 = 9.9\)
• New range with \(23.1\): \(23.1 - 1.8 = 21.3\)
• The range increases by \(11.4\) units (more than doubling its original value).

Therefore, adding an extreme outlier has the biggest effect on the range.

Answer:

If the next month's rainfall is 23.1 inches, this will have the biggest effect on the <blank>range</blank>