Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.

Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.

Correct Answer: 6

Step 1: Arrange the data set in ascending order. The data set is already arranged: 1, 3, 7, 8, 9, 10.
Step 2: Find the median of the data set. The median is the middle value. Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers: (7 + 8) / 2 = 7.5.
Step 3: Divide the data set into two halves. The lower half is 1, 3, 7 and the upper half is 8, 9, 10.
Step 4: Find Q1 (the first quartile) which is the median of the lower half. The lower half is 1, 3, 7. The median is 3.
Step 5: Find Q3 (the third quartile) which is the median of the upper half. The upper half is 8, 9, 10. The median is 9.
Step 6: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. Substitute the values: IQR = 9 - 3.
Step 7: Perform the subtraction: 9 - 3 = 6.

Interquartile Range (IQR) – The IQR 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.