Question - Calculating Interquartile Range of a Dataset
Solution:
To find the interquartile range (IQR) of a dataset, you need to find the difference between the third quartile (Q3) and the first quartile (Q1).First, let's arrange the given data in ascending order if it is not already sorted:1, 2, 4, 4, 4, 4, 4, 8, 8.The dataset is already sorted. The next step is to find Q1 and Q3:- The first quartile (Q1) is the median of the first half of the data. Since there are 9 data points, the first half will consist of the first 4 data points. Q1 is the median of 1, 2, 4, 4, which is the average of the 2nd and 3rd points, (2+4)/2 = 3.- The third quartile (Q3) is the median of the second half of the data. The second half of the dataset after excluding the median (4, in this case) is 4, 4, 8, 8. The median of these four numbers is the average of the 2nd and 3rd points, (4+4)/2 = 4.Now, we find the IQR:IQR = Q3 - Q1 = 4 - 3 = 1.So, the interquartile range of the given dataset is 1.
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