To find the interquartile range (IQR) of the given data set, we first need to organize the data in ascending order and identify the quartiles.
The given data set is:
25272828374147656565
Let's sort these numbers in ascending order:
Sorted Data: 25, 26, 27, 27, 28, 28, 34, 37, 41, 46, 47, 56, 56, 65, 65
Next, we need to find the first quartile (Q1) and the third quartile (Q3).
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Find Q1 (first quartile): Q1 is the median of the first half of the data. The first half of the sorted data is: 25, 26, 27, 27, 28, 28, 34 Since there are 7 numbers, the median (Q1) is the 4th number: Q1 = 27
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Find Q3 (third quartile): Q3 is the median of the second half of the data. The second half of the sorted data is: 37, 41, 46, 47, 56, 56, 65, 65 Since there are 8 numbers, the median (Q3) is the average of the 4th and 5th numbers: Q3 = (46 + 47) / 2 = 46.5
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Calculate the interquartile range (IQR): IQR = Q3 - Q1 = 46.5 - 27 = 19.5
Thus, the interquartile range (IQR) of the given data set is 19.5.