Answer :
Final answer:
The interquartile range (IQR) of the ordered data set (24, 34, 37, 41, 99, 107, 113, 114, 119) is calculated by finding the first quartile (Q1) and third quartile (Q3), then subtracting Q1 from Q3, resulting in an IQR of 78. This does not match the given options. The correct option is not listed here.
Explanation:
The question asks us to calculate the interquartile range (IQR) for the given data set: 37, 34, 24, 41, 113, 99, 119, 107, 114. The IQR is a measure of statistical dispersion and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a data set.
To find the IQR, we first need to order the data set from least to greatest and find the medians for the lower and upper halves of the data to determine Q1 and Q3. Here's the ordered data: 24, 34, 37, 41, 99, 107, 113, 114, 119.
The median of this 9-number data set is the middle number, which is 99. This divides the data into a lower half (24, 34, 37, 41) and an upper half (107, 113, 114, 119). The median of the lower half is (34 + 37)/2 = 35.5, which is Q1. The median of the upper half is (113 + 114)/2 = 113.5, which is Q3.
Finally, the IQR is calculated by subtracting Q1 from Q3: 113.5 - 35.5 = 78. Therefore, the IQR of the data set is 78. However, this result does not match any of the options a-d given in the question.
