Question

0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10

what is the IQR and the median

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the interquartile range (IQR) and median of the given dataset, we first need to arrange the data in ascending order:

0.5, 1.0, 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.5, 3.0, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 8.0, 10

The median is the middle value when the data set is ordered. In this case, there are 18 values, so the median will be the average of the 9th and 10th values:

Median = (2.5 + 3.0) / 2 = 2.75

To find the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the first half of the data, and Q3 is the median of the second half of the data.

Q1 = Median of the first half = (1.0 + 1.0 + 1.0 + 1.5 + 2.0 + 2.0 + 2.0) / 7 = 1.5
Q3 = Median of the second half = (4.0 + 5.0 + 6.0 + 8.0 + 10) / 5 = 6.0

Then, the IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1):

IQR = Q3 - Q1 = 6.0 - 1.5 = 4.5

Therefore, the median of the data set is 2.75 and the interquartile range (IQR) is 4.5.