Question

The average temperature in December in Washington DC from 1993 to 1998 are given as a data set 38 144 235 643 zero 41 zero44.4 find the intrerquartile range of the data set express your answer as a decimal rounded to the nearest 10th

Answer 1

To find the interquartile range (IQR) of the data set, we first need to order the data and calculate the first quartile (Q1) and the third quartile (Q3).

The provided data set is:
\[ 38, 144, 235, 643, 0, 41, 44.4 \]

1. **Order the data**:
\[ 0, 0, 38, 41, 44.4, 144, 235, 643 \]

2. **Determine Q1 and Q3**:
- The data set has 8 values. To find Q1 and Q3, we first split the data into two halves.
- The lower half is:
\[ 0, 0, 38, 41 \]
- The upper half is:
\[ 44.4, 144, 235, 643 \]

3. **Calculate Q1** (the median of the lower half):
- The median of \(0, 0, 38, 41\):
- There are 4 numbers, so the median is the average of the 2nd and 3rd values:
\[ Q1 = \frac{0 + 38}{2} = 19 \]

4. **Calculate Q3** (the median of the upper half):
- The median of \(44.4, 144, 235, 643\):
- There are 4 numbers, so the median is the average of the 2nd and 3rd values:
\[ Q3 = \frac{144 + 235}{2} = \frac{379}{2} = 189.5 \]

5. **Calculate the IQR**:
\[ \text{IQR} = Q3 - Q1 = 189.5 - 19 = 170.5 \]

Finally, rounding to the nearest tenth, the interquartile range (IQR) is:
\[
\boxed{170.5}
\]