To calculate the interquartile range (IQR), you need to find the first quartile (Q1) and the third quartile (Q3) of the data set, and then subtract Q1 from Q3.
The data set provided is: 16, 26, 34, 38, 50, 60, 69
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Order the data (already ordered): 16, 26, 34, 38, 50, 60, 69
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Find Q1 and Q3:
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Q1 is the median of the first half of the data (the lower half). The first half is: 16, 26, 34 The median of this set (Q1) is the middle value, which is 26.
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Q3 is the median of the second half of the data (the upper half). The second half is: 38, 50, 60, 69 The median of this set (Q3) is the average of the two middle values (50 and 60): \[ Q3 = \frac{50 + 60}{2} = \frac{110}{2} = 55 \]
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Calculate the IQR: \[ IQR = Q3 - Q1 = 55 - 26 = 29 \]
Thus, the interquartile range (IQR) is 29.