In a box-and-whisker plot, the upper quartile (Q3) is represented by the line or point at the upper edge of the box. This corresponds to the 75th percentile of the data, meaning that 75% of the data falls below this value.
Given the responses you provided (−3, -2, -0.5, 0, 0.5, 1), we need to determine the upper quartile from this dataset.
First, let's arrange the data in order:
-3, -2, -0.5, 0, 0.5, 1
Next, calculate the position of the upper quartile (Q3). Since there are 6 data points, the position of Q3 can be found using this formula:
\[ Q_3 = \frac{3(n + 1)}{4} \] where \( n \) is the number of observations.
Substituting in the values:
\[ Q_3 = \frac{3(6 + 1)}{4} = \frac{21}{4} = 5.25 \]
Since 5.25 is not a whole number, we need to take the average of the values in positions 5 and 6.
- Position 5: 0.5
- Position 6: 1
Now, take the average of these two values:
\[ Q_3 = \frac{0.5 + 1}{2} = \frac{1.5}{2} = 0.75 \]
Therefore, the upper quartile (Q3) of the data illustrated in the box-and-whisker plot is 0.75.