Identify the upper quartile of the data illustrated in the box-and-whisker plot.
−3
−2
- 2
−0.5
1
We cannot determine the upper quartile from the data provided. The upper quartile is the median of the upper half of the data set, and we need more values to calculate it.
To identify the upper quartile of the data illustrated in the box-and-whisker plot, we need to locate the data point that represents the 75th percentile.
Looking at the given data:
-3, -2, -2, -0.5, 1
We can arrange the data in ascending order:
-3, -2, -2, -0.5, 1
Next, we need to find the position of the upper quartile. Since the upper quartile represents the 75th percentile, we have 75% of the data below this point.
There are a total of 5 data points, so 75% of 5 is (75/100) * 5 = 3.75.
Since we cannot have a fractional position, we round up to the nearest whole number, giving us position 4.
In the ordered data set, the 4th data point is -0.5. Therefore, the upper quartile of the data is -0.5.