To find the interquartile range (IQR) of the dataset, we first need to order the data from smallest to largest and then find the first quartile (Q1) and the third quartile (Q3).
Here is the dataset in ascending order:
35.6, 38.1, 41.0, 43.0, 44.2, 44.4
Step 1: Find Q1 and Q3
- Q1 (the first quartile) is the median of the first half of the data.
- Q3 (the third quartile) is the median of the second half of the data.
Since we have 6 data points, the first half consists of the first 3 numbers, and the second half consists of the last 3 numbers:
- First half: 35.6, 38.1, 41.0
- Second half: 43.0, 44.2, 44.4
Finding Q1:
The median of the first half (35.6, 38.1, 41.0) is: \[ Q1 = 38.1 \quad (\text{the middle value}) \]
Finding Q3:
The median of the second half (43.0, 44.2, 44.4) is: \[ Q3 = 44.2 \quad (\text{the middle value}) \]
Step 2: Calculate the IQR
The interquartile range is calculated as follows: \[ IQR = Q3 - Q1 \] Substituting the values we found: \[ IQR = 44.2 - 38.1 = 6.1 \]
Thus, the interquartile range of the dataset is 6.1.