Ask a New Question
Menu

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 \(38.1, 44.2, 35.6, 43.0, 41.0, 44.4\), we will follow these steps:

  1. Sort the data in ascending order:

    • \(35.6, 38.1, 41.0, 43.0, 44.2, 44.4\)

  2. Find the first quartile (Q1):

    • Q1 is the median of the first half of the data. The first half is \(35.6, 38.1, 41.0\).
    • The median of \(35.6, 38.1, 41.0\) (3 numbers) is the middle number, which is \(38.1\).

  3. Find the third quartile (Q3):

    • Q3 is the median of the second half of the data. The second half is \(43.0, 44.2, 44.4\).
    • The median of \(43.0, 44.2, 44.4\) (3 numbers) is the middle number, which is \(44.2\).

  4. Calculate the interquartile range (IQR): \[ \text{IQR} = Q3 - Q1 = 44.2 - 38.1 = 6.1 \]

Thus, the interquartile range of the dataset is \( \boxed{6.1} \).