In the data set below, what is the interquartile range?
124252626868729494
To find the interquartile range (IQR), we first need to find the 1st and 3rd quartiles.
1. Arrange the data in ascending order:
12, 24, 25, 26, 26, 26, 26, 29, 47, 49, 68, 72, 94
2. Find the median (middle value) of the data set. Since there are 13 values, the median will be the average of the 7th and 8th values:
Median = (26 + 26) / 2 = 26
3. Divide the data set into two halves, and find the median of each half
- Lower half: 12, 24, 25, 26, 26, 26 (since there are 6 values, the median will be the average of the 3rd and 4th values): (25 + 26) / 2 = 25.5
- Upper half: 29, 47, 49, 68, 72, 94 (since there are 6 values, the median will be the average of the 3rd and 4th values): (49 + 68) / 2 = 58.5
4. Find the 1st quartile (Q1) and 3rd quartile (Q3) using the medians of the lower and upper halves:
Q1 = 25.5
Q3 = 58.5
5. Calculate the IQR:
IQR = Q3 - Q1 = 58.5 - 25.5 = 33
Therefore, the interquartile range of the data set is 33.