The average temperatures in December in Washington, D.C., from 1993 to 1998 are given as a dataset.
38.1, 44.2, 35.6, 43.0, 41.0, 44.4
Find the interquartile range of the dataset.
The interquartile range of the dataset is ___.
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3) of the dataset.
1. Arrange the dataset in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
2. Calculate the median (Q2) of the dataset:
Q2 = (41.0 + 43.0) / 2 = 42.0
3. Split the dataset into two halves:
Lower half: 35.6, 38.1, 41.0
Upper half: 43.0, 44.2, 44.4
4. Find the median of the lower half (Q1):
Q1 = (38.1 + 41.0) / 2 = 39.55
5. Find the median of the upper half (Q3):
Q3 = (43.0 + 44.2) / 2 = 43.6
6. Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 43.6 - 39.55
IQR = 4.05
Therefore, the interquartile range of the dataset is 4.05.