The range is the difference between the largest and smallest values in the dataset. The smallest value is 21 and the largest value is 44, so the range is:
44 - 21 = 23
To find the IQR, we first need to find the median of the dataset. Since there are 12 values, the median will be the average of the 6th and 7th values when the dataset is arranged in order:
21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44
The 6th and 7th values are both 32, so the median is 32.
Next, we need to find the quartiles of the dataset. The first quartile, Q1, is the median of the values below the median. The third quartile, Q3, is the median of the values above the median.
First, we find the median of the values below the median (i.e. the first half of the dataset):
21, 24, 25, 27, 30, 32
The 3rd and 4th values are both 25, so Q1 is 25.
Next, we find the median of the values above the median (i.e. the second half of the dataset):
33, 34, 34, 36, 41, 44
The 3rd and 4th values are both 34, so Q3 is 34.
The IQR is the difference between Q3 and Q1:
34 - 25 = 9
Find these measures of variability for the given dataset: range and IQR.
21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44
1 answer