Question - Calculating Interquartile Range (IQR) of a Dataset
Solution:
To find the interquartile range (IQR) of the dataset, follow these steps:1. **Order the Data**: The data in the image is already ordered from smallest to largest.2. **Find the Median**: The median is the middle number of the dataset. If the number of observations is odd, the median is the middle number. If the number of observations is even, the median is the average of the two middle numbers. The dataset has 13 numbers, so the median is the 7th number: 22.3. **Split the Data into Quarters**: After finding the median, split the data into two halves. For the lower half (below the median), don't include the median if the number of data points is odd. - Lower half: 10, 14, 16, 20, 20 - Upper half: 25, 30, 36, 42, 434. **Find the First Quartile (Q1)**: The first quartile is the median of the lower half of the data. Since there are 5 numbers in the lower half, the median is the third number: 16.5. **Find the Third Quartile (Q3)**: The third quartile is the median of the upper half of the data. Similarly, as there are 5 numbers in the upper half, the median is the third number: 36.The interquartile range is the difference between the third quartile and the first quartile:IQR = Q3 - Q1IQR = 36 - 16IQR = 20The interquartile range of the dataset is 20.
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