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.

Answer 1

incorrecto

Answer 2

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

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:
For an even number of observations, the median is the average of the middle two values. In this case, the middle two values are 41.0 and 43.0, so the median is (41.0 + 43.0) / 2 = 42.0.

3. Find Q1 (the median of the lower half of the dataset):
On the lower half of the dataset (35.6, 38.1), the median is (35.6 + 38.1) / 2 = 36.85.

4. Find Q3 (the median of the upper half of the dataset):
On the upper half of the dataset (43.0, 44.2, 44.4), the median is (44.2 + 44.4) / 2 = 44.3.

5. Calculate the IQR:
IQR = Q3 - Q1
IQR = 44.3 - 36.85
IQR = 7.45

Therefore, the interquartile range of the dataset is 7.45.

Answer 3

My 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 (Q2):
The median of the dataset is (41.0 + 43.0) / 2 = 42.0

3. Find Q1 (the median of the lower half of the dataset):
On the lower half of the dataset (35.6, 38.1, 41.0), the median is (38.1) = 38.1.

4. Find Q3 (the median of the upper half of the dataset):
On the upper half of the dataset (43.0, 44.2, 44.4), the median is (44.2) = 44.2.

5. Calculate the IQR:
IQR = Q3 - Q1
IQR = 44.2 - 38.1
IQR = 6.1

Therefore, the correct interquartile range of the dataset is 6.1.