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![In the data set below, what is the interquartile range?
{:[1,1,3,1,6,3,1,5]:}](https://blblobstorage.blob.core.windows.net/solver-b2c/4a95bd16-eddc-11ee-9ceb-667af2bd5b85.png)
In the data set below, what is the interquartile range?
Full solution
Q. In the data set below, what is the interquartile range?
- Arrange Data Set: First, we need to arrange the data set in ascending order.The given data set is: Arranged in ascending order:
- Find Median: Next, we find the median (the middle value) of the data set to divide it into two halves. Since there are numbers, the median will be the average of the th and th values.Median
- Find Lower Quartile: Now we find the lower quartile (), which is the median of the lower half of the data set (excluding the median if the number of data points is odd). The lower half of the data set is \{, , , \}.Lower quartile () = median of \{, , , \} =
- Find Upper Quartile: We then find the upper quartile (Q), which is the median of the upper half of the data set (excluding the median if the number of data points is odd). The upper half of the data set is .Upper quartile (Q) = median of = =
- Calculate Interquartile Range: Finally, we calculate the interquartile range (IQR), which is the difference between the upper and lower quartiles.
