What does the interquartile range describe?. a) The ranges of the lower 25% and the upper 25% of the observations. b) The range of the upper 50% of the observations. c) The range of the middle 50% of the observations. d) The range of the lower 50% of the observations
The correct answer is c) The interquartile range (IQR) describes the range of the middle 50% of the observations in a data set
The correct answer is c) The interquartile range (IQR) describes the range of the middle 50% of the observations in a data set.
The IQR is a measure of dispersion that is often used in statistics to describe the spread of data. To calculate the IQR, we first need to find the lower quartile (Q1) and the upper quartile (Q3) of the data set.
Q1 represents the point below which 25% of the data falls, and Q3 represents the point below which 75% of the data falls. The IQR is then calculated as the difference between Q3 and Q1.
For example, if we have a data set of temperatures in a week: 10, 12, 13, 15, 16, 18, 20, 22, 25, 30.
First, we need to arrange the data in ascending order: 10, 12, 13, 15, 16, 18, 20, 22, 25, 30.
Next, we find Q1 and Q3. Since we have 10 data points, Q1 would be the (10 + 1) * 0.25 = 2.75th value. The value at this position is between 12 and 13, so we can estimate Q1 as 12 + (13-12) * 0.75 = 12.75.
Similarly, Q3 would be the (10 + 1) * 0.75 = 8.25th value. The value at this position is between 22 and 25, so we can estimate Q3 as 22 + (25-22) * 0.25 = 22.75.
Finally, we calculate the IQR as Q3 – Q1 = 22.75 – 12.75 = 10.
Therefore, the interquartile range for this data set is 10, which represents the range of the middle 50% of the observations.
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