Question - Calculating Interquartile Range
Solution:
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) in a data set.To find the IQR, follow these steps:1. Order the data set from smallest to largest (which is already done in this case).2. Divide the data set into quartiles. Q1 is the median of the first half of the data, and Q3 is the median of the second half.3. Calculate Q1 and Q3, and then find the difference between them.Let's go through the steps with the given data set:10, 25, 31, 40, 45, 51, 59, 67, 96, 98There are 10 data points, so we can exactly divide this set into two halves for finding Q1 and Q3:First half (for Q1): 10, 25, 31, 40, 45Second half (for Q3): 51, 59, 67, 96, 98Now let's find Q1, the median of the first half:Q1 = 31 (since 31 is the middle value in the first half)And Q3, the median of the second half:Q3 = 67 (since 67 is the middle value in the second half)Finally, calculate the IQR:IQR = Q3 - Q1IQR = 67 - 31IQR = 36So, the interquartile range of the given data set is 36.
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