Question - Calculating Interquartile Range from Data Set
Solution:
To find the interquartile range of the data set, you must first find the first quartile (Q1), which is the median of the lower half of the data, and the third quartile (Q3), which is the median of the upper half of the data. The interquartile range is then calculated by subtracting Q1 from Q3.The data set provided is:36, 44, 44, 68, 71, 75Step 1: Find the median to separate the lower and upper halves of the data. Since there's an even number of data points, the median is the average of the middle two values. The middle values are the third and fourth values:Median = (44 + 68) / 2 = 112 / 2 = 56Step 2: Find Q1, the median of the lower half of the data (not including the median of the dataset if the number of observations is odd).The lower half of the data is 36, 44, and 44. The median of these values is directly the second number (since there are an odd number of data points in the lower half):Q1 = 44Step 3: Find Q3, the median of the upper half of the data (not including the median of the dataset if the number of observations is odd).The upper half of the data is 68, 71, and 75. The median of these values is directly the second number:Q3 = 71Step 4: Calculate the interquartile range (IQR), which is Q3 - Q1.IQR = Q3 - Q1IQR = 71 - 44IQR = 27The interquartile range for the provided data set is 27.
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