Question - Calculating Interquartile Range (IQR) for a Data Set
Solution:
To find the interquartile range (IQR) for a given data set, you need to subtract the first quartile (Q1) from the third quartile (Q3).The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half.The given data set: 1, 5, 5, 8, 8, 9, 9Step 1: Find the median, which is the middle value when the data set is ordered. In this case, the median is 8 (there are 3 numbers to the left and 3 numbers to the right).Step 2: Find Q1 and Q3. - For Q1, you take the lower half of the data set, which is 1, 5, 5. The median of this half is 5.- For Q3, you take the upper half of the data set, which is 8, 9, 9. The median of this half is 9.Step 3: Subtract Q1 from Q3 to get the IQR.IQR = Q3 - Q1 = 9 - 5 = 4So, the interquartile range of the given data set is 4.
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