Question

Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

Answer 1

The five number summary and interquartile range for the data-set is given by:

• Minimum: 48

• Lower quartile: 54.

• Median: 63.5.

• Upper quartile: 74

• Maximum: 80.

• Interquartile range: 20

How to find the five number summary and interquartile range of the data-set?

The five number summary is composed by the minimum and maximum value, and the first quartile, median and third quartile. As for each of these data, they are explained below.

• The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.

• The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

• The first quartile is the median of the first half of the data-set.

• The third quartile is the median of the second half of the data-set.

• The interquartile range is the difference of the third quartile and the first quartile.

In this problem, we have that:

• The minimum value is the smallest value, of 48.

• The maximum value is the smallest value, of 80.

• The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.

• The first quartile is the median of the five elements of the first half, hence it is of 54.

• The third quartile is the median of the five elements of the second half, hence it is of 74.

• The IQR is the difference between the quartiles, hence 74 - 54 = 20.

More can be learned about five number summaries at brainly.com/question/17110151

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