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
8.4
the difference between the first quartile (Q1) and the third quartile (Q3) of the dataset. To find the interquartile range, we need to first calculate Q1 and Q3.
Step 1: Sort the dataset in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
Step 2: Calculate the median (M) of the dataset. Since the dataset has an even number of values, we take the average of the two middle values:
M = (41.0 + 43.0) / 2 = 42.0
Step 3: Calculate Q1. Q1 is the median of the lower half of the dataset.
Q1 = (35.6 + 38.1) / 2 = 36.85
Step 4: Calculate Q3. Q3 is the median of the upper half of the dataset.
Q3 = (44.2 + 44.4) / 2 = 44.3
Step 5: Calculate the interquartile range (IQR). IQR = Q3 - Q1.
IQR = 44.3 - 36.85 = 7.45
Therefore, the interquartile range of the dataset is 7.45.