Find the lower quartile of the data set {42, 49, 91, 42, 94, 73, 93, 67, 55, 54, 78, 82}.Group of answer choices51.54986.554
Question
Find the lower quartile of the data set {42, 49, 91, 42, 94, 73, 93, 67, 55, 54, 78, 82}.
Group of answer choices
51.5
49
86.5
54
Solution
To find the lower quartile (Q1) of the data set, follow these steps:
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First, arrange the data set in ascending order: {42, 42, 49, 54, 55, 67, 73, 78, 82, 91, 93, 94}.
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The lower quartile (Q1) is the median of the lower half of the data. Since there are 12 numbers in the data set, the lower half will be the first 6 numbers: {42, 42, 49, 54, 55, 67}.
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To find the median of these 6 numbers, take the average of the middle two numbers. In this case, the middle two numbers are 49 and 54.
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The average of 49 and 54 is (49 + 54) / 2 = 51.5.
So, the lower quartile (Q1) of the data set is 51.5.
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