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Here are yesterday's high temperatures (in degrees Fahrenheit) in 14 U.S. cities.49,  56,  56,  61,  61,  64,  65,  67,  67,  68,  74,  77,  80,  82Notice that the temperatures are ordered from least to greatest.Give the median, lower quartile, and upper quartile for the data set.(a) Median: (b) Lower quartile: (c) Upper quartile:

Question

Here are yesterday's high temperatures (in degrees Fahrenheit) in 14 U.S. cities.49,  56,  56,  61,  61,  64,  65,  67,  67,  68,  74,  77,  80,  82Notice that the temperatures are ordered from least to greatest.Give the median, lower quartile, and upper quartile for the data set.(a) Median: (b) Lower quartile: (c) Upper quartile:

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Solution

(a) Median: The median is the middle number in a sorted, ascending or descending, list of numbers. In this case, since we have 14 numbers, the median will be the average of the 7th and 8th numbers. So, (65+67)/2 = 66.

(b) Lower quartile: The lower quartile, also known as the first quartile, is the median of the lower half of the data set. This does not include the median of the overall data set. In this case, the lower half of the data set is 49, 56, 56, 61, 61, 64, 65. The median of this data set is 61.

(c) Upper quartile: The upper quartile, also known as the third quartile, is the median of the upper half of the data set. This does not include the median of the overall data set. In this case, the upper half of the data set is 67, 67, 68, 74, 77, 80, 82. The median of this data set is 74.

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