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.
(1 point)
The interquartile range of the dataset is
.
7.4.
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).
1. First, we need to arrange the data in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
2. Next, find the median of the dataset. Since the dataset has an even number of values, the median is the average of the two middle values:
(41.0 + 43.0) / 2 = 42.0
3. Now, we divide the dataset into two halves.
- For the lower half: 35.6, 38.1, 41.0
- For the upper half: 43.0, 44.2, 44.4
4. Next, find the median of each half.
- Q1 = (38.1 + 41.0) / 2 = 39.55
- Q3 = (43.0 + 44.2) / 2 = 43.6
5. Finally, calculate the interquartile range by subtracting Q1 from Q3:
43.6 - 39.55 = 4.05
Therefore, the interquartile range of the dataset is 4.05.