Problem

Here are yesterday's high temperatures (in Fahrenheit) in 13 U.S. cities. $47,50,51,51,61,62,66,67,68,69,75,77,79$ 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: \[ \times \quad 5 \]

Solution

Step 1 :The five-number summary of a dataset consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The interquartile range (IQR) is the difference between the third quartile and the first quartile.

Step 2 :To calculate these, we first need to find the minimum and maximum, which are the smallest and largest numbers in the dataset, respectively.

Step 3 :Next, we find the median, which is the middle number when the data is arranged in ascending order. If there is an even number of data points, the median is the average of the two middle numbers.

Step 4 :The first quartile (Q1) is the median of the lower half of the data (not including the median if the number of data points is odd), and the third quartile (Q3) is the median of the upper half of the data.

Step 5 :Finally, the interquartile range (IQR) is calculated as Q3 - Q1.

Step 6 :The five-number summary for the data set is: Minimum: \(\boxed{47}\), Lower quartile (Q1): \(\boxed{51}\), Median: \(\boxed{66}\), Upper quartile (Q3): \(\boxed{69}\), Maximum: \(\boxed{79}\)

Step 7 :The interquartile range (IQR) for the data set is: \(\boxed{18}\)

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