Question

Calculate the median and IQR (Interquartile Range) for the dataset {4, 5, 7, 8, 8, 9, 10, 12, 14}.

A) Median = 8, IQR = 5
B) Median = 9, IQR = 4
C) Median = 8, IQR = 6
D) Median = 10, IQR = 5

Answer 1

The median of the dataset {4, 5, 7, 8, 8, 9, 10, 12, 14} is 8, and the interquartile range (IQR) is 4.

Step-by-step explanation:

To calculate the median and the interquartile range (IQR) for the given dataset {4, 5, 7, 8, 8, 9, 10, 12, 14}, we first need to order the dataset, which is already ordered in this case. The median is the middle number in the dataset, which in this case is 8 because it is the fifth number in a list of nine numbers. To find the first quartile (Q1) and third quartile (Q3), we need to find the medians of the lower and upper halves of the dataset, excluding the overall median. For the lower half (4, 5, 7, 8), the median is 6, and for the upper half (8, 9, 10, 12, 14), the median is 10. Therefore, the IQR is Q3 - Q1, which is 10 - 6, giving us an IQR of 4.