If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?

If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?

Step 1: Arrange the data set in ascending order. The data set is already arranged: {5, 7, 8, 9, 10}.
Step 2: Find the median of the data set. The median is the middle number. For {5, 7, 8, 9, 10}, the median is 8.
Step 3: Divide the data set into two halves. The lower half is {5, 7} and the upper half is {9, 10}.
Step 4: Find Q1 (the first quartile) which is the median of the lower half {5, 7}. The median of {5, 7} is 7.
Step 5: Find Q3 (the third quartile) which is the median of the upper half {9, 10}. The median of {9, 10} is 9.
Step 6: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. Here, IQR = 9 - 7.
Step 7: Perform the subtraction: 9 - 7 = 2.

Interquartile Range (IQR) – The interquartile range is a measure of statistical dispersion, calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a data set.
Quartiles – Quartiles are values that divide a data set into four equal parts, with Q1 being the median of the first half and Q3 being the median of the second half.