Question

The annual rate of return (in %) for a random sample of 11 high-risk mutual funds was obtained. The data

were recorded as follows:
13 -6 179 -15 12 -20 -115 -10 18
Obtain Tukey's five-number summary for these data.

Answer 1

To obtain Tukey's five-number summary, we arrange the mutual fund returns in ascending order, identify the minimum, first quartile, median, third quartile, and maximum. The five-number summary is -20%, -10%, 12%, 17%, 115%.

Step-by-step explanation:

The question asks to obtain Tukey's five-number summary for a sample of 11 high-risk mutual funds with the given return percentages. First, we need to organize the data in ascending order, then find the minimum, first quartile, median, third quartile, and maximum values to complete the summary.

1. Arrange the returns in ascending order: -20, -15, -10, -6, 9, 12, 13, 15, 17, 18, 115.
2. Minimum value: -20%
3. First quartile (Q1): -10% (the median of the first half of the data)
4. Median: 12% (the middle value of the ordered dataset)
5. Third quartile (Q3): 17% (the median of the second half of the data)
6. Maximum value: 115%

Tukey's five-number summary for these mutual fund returns is: -20%, -10%, 12%, 17%, 115%.