Question - Calculating Quartiles from a Dataset
Solution:
To find the lower quartile, median, and upper quartile from a set of numbers, you first ensure that the numbers are ordered from smallest to largest, which they already are in the image you provided:14, 20, 20, 31, 38, 45, 54, 81, 81, 87, 92There are 11 numbers in this dataset. The median (the middle number) is easy to find because there is an odd number of data points. The median will be the value in the middle of the dataset:Median: Since there are 11 numbers, the median will be the 6th number (as 5 numbers are on either side):14, 20, 20, 31, 38, (45), 54, 81, 81, 87, 92So, the median is 45.For the quartiles, we divide the dataset into four equal parts. The lower quartile (Q1) is the median of the lower half of the dataset (not including the median if there is an odd number of data points), and the upper quartile (Q3) is the median of the upper half of the dataset.Lower quartile: The lower half of the dataset (before the median) is: 14, 20, 20, 31, 38Since there are 5 numbers in this lower half, the lower quartile is the middle value, which is the 3rd number:14, 20, (20), 31, 38So, the lower quartile is 20.Upper quartile: The upper half of the dataset (after the median) is: 54, 81, 81, 87, 92Again, there are 5 numbers in this upper half, so the upper quartile will also be the middle value, which is the 3rd number:54, 81, (81), 87, 92So, the upper quartile is 81.In summary:Lower quartile (Q1) = 20Median (Q2) = 45Upper quartile (Q3) = 81
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