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Difficulty: EasyMeasures of Dispersion and Position (Range, IQR, Standard Deviation, Percentiles)

The high temperatures, in degrees Fahrenheit, recorded in a city over a 7-day period were 64, 58, 75, 67, 61, 83, and 72. What is the interquartile range of these temperatures, in degrees Fahrenheit?

Answer: 14 degrees Fahrenheit

Answer

The interquartile range of the recorded temperatures is 14.
To calculate the interquartile range, first arrange the dataset in ascending order: 58, 61, 64, 67, 72, 75, 83. The median of the 7 values is 67. The first quartile (Q1Q_1) is the median of the lower three values (58, 61, 64), which is 61. The third quartile (Q3Q_3) is the median of the upper three values (72, 75, 83), which is 75. Subtracting Q1Q_1 from Q3Q_3 yields an interquartile range of 75−61=1475 - 61 = 14.

Step-by-Step Solution

1
Order the dataset from least to greatest
58, 61, 64, 67, 72, 75, 83
Finding quartiles requires data to be arranged in ascending order.
2
Find the first quartile (Q1Q_1) and third quartile (Q3Q_3)
Q1=61Q_1 = 61 and Q3=75Q_3 = 75
The median of the dataset (the 4th value) is 67. The lower half of the data consists of 58, 61, 64 (median 61), and the upper half consists of 72, 75, 83 (median 75).
3
Compute the difference between Q3Q_3 and Q1Q_1
75−61=1475 - 61 = 14
The interquartile range is defined as IQR=Q3−Q1IQR = Q_3 - Q_1.

Key Concept

Interquartile Range (IQR)
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Topics

Measures of Dispersion and Position (Range, IQR, Standard Deviation, Percentiles)

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