To find the interquartile range (IQR) of the bass weights, we first need to identify the first quartile (Q1) and the third quartile (Q3).
Given the weights:
- 4 lb
- 6 lb
- 8 lb
- 10 lb
- 12 lb
- 14 lb
First, we will arrange the weights in ascending order, which they already are.
Step 1: Find median (Q2) The median (Q2) is the middle value. Since there are 6 values, the median will be the average of the 3rd and 4th values.
\[ \text{Median} (Q2) = \frac{8 + 10}{2} = 9 \text{ lb} \]
Step 2: Find Q1 Q1 is the median of the first half of the data (the lower half):
Lower half: 4 lb, 6 lb, 8 lb
The median of this subset (Q1) is the second value: \[ Q1 = 6 \text{ lb} \]
Step 3: Find Q3 Q3 is the median of the second half of the data (the upper half):
Upper half: 10 lb, 12 lb, 14 lb
The median of this subset (Q3) is the second value: \[ Q3 = 12 \text{ lb} \]
Step 4: Calculate the Interquartile Range (IQR) The IQR is calculated as follows: \[ \text{IQR} = Q3 - Q1 = 12 \text{ lb} - 6 \text{ lb} = 6 \text{ lb} \]
Thus, the interquartile range of the weights is 6 pounds.