Question - Calculating Quartiles of a Data Set
Solution:
To solve the given problem, we need to find the lower quartile (Q1), median (Q2), and upper quartile (Q3) of the provided data set.The data set is as follows:15, 25, 42, 42, 42, 48, 74, 84, 90, 90, 91First, let's arrange the data in ascending order, which is already done. There are 11 numbers in this data set.To find the median (Q2), we locate the middle number in the set. Since there are 11 numbers, the median will be the 6th number (as 11 + 1 divided by 2 gives us 6). Therefore, the median is 48.Next, we divide the data set into two halves to find the lower and upper quartiles. The lower half for the lower quartile will be the numbers before the median, and the upper half for the upper quartile will be the numbers after the median:Lower half (before median): 15, 25, 42, 42, 42Upper half (after median): 74, 84, 90, 90, 91Now, to find the lower quartile (Q1), we find the median of the lower half of the data set. Because there are 5 numbers in the lower half, the middle one is the 3rd, making Q1 equal to 42.To find the upper quartile (Q3), we do the same for the upper half of the data. There are 5 numbers in the upper half, so the middle one is also the 3rd number in the upper half, making Q3 equal to 90.Therefore, the lower quartile (Q1) is 42, the median (Q2) is 48, and the upper quartile (Q3) is 90.
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