Question

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
.
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Answer 1

incorrect

Answer 2

The given dataset is: 38.1, 44.2, 35.6, 43.0, 41.0, 44.4

To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).

1. Arrange the data in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4

2. Calculate the median of the dataset:
Median = (41.0 + 43.0) / 2 = 42.0

3. Find the median of the lower half of the data (Q1):
Q1 = (38.1 + 41.0) / 2 = 39.55

4. Find the median of the upper half of the data (Q3):
Q3 = (43.0 + 44.2) / 2 = 43.6

5. 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.

Answer 3

Apologies for the mistake. Let's recalculate the interquartile range correctly:

Given dataset: 38.1, 44.2, 35.6, 43.0, 41.0, 44.4

1. Arrange the data in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4

2. Find the median of the dataset:
Median = (41.0 + 43.0) / 2 = 42.0

3. Identify the lower quartile (Q1) and upper quartile (Q3) positions:
Q1 position = (n + 1) / 4 = (6 + 1) / 4 = 1.75 (between the 1st and 2nd values)
Q3 position = 3(n + 1) / 4 = 3(6 + 1) / 4 = 5.25 (between the 5th and 6th values)

4. Calculate Q1 and Q3:
Q1 = (38.1 + 38.1) / 2 = 38.1
Q3 = (44.2 + 44.4) / 2 = 44.3

5. Find the interquartile range (IQR):
IQR = Q3 - Q1 = 44.3 - 38.1 = 6.2

Therefore, the correct interquartile range of the dataset is 6.2.