Question

Find these measures of variability for the given dataset: IQR.

21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44 (1 point)

Answer 1

To find the IQR (Interquartile Range) for the given dataset, first we need to find the first quartile (Q1) and third quartile (Q3).

1. Arrange the data in ascending order:
21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44

2. Determine the median:
Since there are 12 data points, the median is the average of the 6th and 7th values:
(32 + 33) / 2 = 32.5

3. Find the first quartile (Q1):
Q1 is the median of the lower half of the data (the values below the median):
(25 + 27) / 2 = 26

4. Find the third quartile (Q3):
Q3 is the median of the upper half of the data (the values above the median):
(34 + 36) / 2 = 35

5. Calculate the IQR:
IQR = Q3 - Q1
IQR = 35 - 26
IQR = 9

Therefore, the Interquartile Range (IQR) for the given dataset is 9.