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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. Express your answer as a decimal rounded to the nearest tenth.

(1 point)
The interquartile range of the dataset is

1 answer

To find the interquartile range (IQR) of the dataset, we first need to arrange the data in ascending order and then identify the first quartile (Q1) and the third quartile (Q3).

The dataset is:

38.1, 44.2, 35.6, 43.0, 41.0, 44.4

Arranging the data in ascending order:

35.6, 38.1, 41.0, 43.0, 44.2, 44.4

Next, we find the quartiles:

  1. Find Q1 (the first quartile): Q1 is the median of the first half of the data. The first half consists of:

35.6, 38.1, 41.0

The median (Q1) is the middle value, which is:

Q1 = 38.1

  1. Find Q3 (the third quartile): Q3 is the median of the second half of the data. The second half consists of:

43.0, 44.2, 44.4

The median (Q3) is the middle value, which is:

Q3 = 44.2

  1. Calculate the interquartile range (IQR): IQR = Q3 - Q1 = 44.2 - 38.1 = 6.1

Thus, the interquartile range of the dataset is:

6.1

So, the answer is:

The interquartile range of the dataset is 6.1.