Question - Calculating Interquartile Range
mathothermedian calculationdata set analysisinterquartile range calculationquartiles position determination
Solution:
To calculate the interquartile range (IQR), you first need to find the first quartile (Q1), which is the median of the lower half of the data, and the third quartile (Q3), which is the median of the upper half of the data. The interquartile range is the difference between Q3 and Q1.First, we will need to determine the position of the quartiles. There are 11 numbers in the data set you provided:10, 25, 31, 40, 45, 51, 51, 59, 67, 96, 98To find Q1, we need the median of the first 5 numbers (since the median - 51 - is not included in either half):10, 25, 31, 40, 45The median of these numbers is 31 (the middle number), so Q1 is 31.To find Q3, we take the median of the last 5 numbers:59, 67, 96, 98The median of these numbers is the average of 67 and 96 because there are an even number of data points:(67 + 96) / 2 = 163 / 2 = 81.5So, Q3 is 81.5.Now, find the IQR by subtracting Q1 from Q3:IQR = Q3 - Q1 = 81.5 - 31 = 50.5Therefore, the interquartile range of the provided data set is 50.5.
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