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.
In the data set below, what is the interquartile range?
124252626868729494
1 answer
1 answer