Calculate the interquartile range of the data set: {7, 3, 10, 8, 4, 1, 8, 6, 5, 8}

Answer: 5

Explanation: The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of a data set.

Steps:

1. Sort the data set: {1, 3, 4, 5, 6, 7, 8, 8, 8, 10}
2. Find Q1: The first quartile (Q1) is the median of the first half of the data. The first half is {1, 3, 4, 5, 6}, so Q1 = 4.
3. Find Q3: The third quartile (Q3) is the median of the second half of the data. The second half is {7, 8, 8, 8, 10}, so Q3 = 8.
4. Calculate IQR: IQR = Q3 – Q1 = 8 – 4 = 4.

Thus, the interquartile range is 4.