Question

The box-and-whisker plot below represents some data set. What percentage of the data values are greater than or equal to 56?
40
50
60
70
80

Answer 1

To determine the percentage of data values that are greater than or equal to 56 from a box-and-whisker plot, we need to understand the distribution of the data represented in the plot.

A box-and-whisker plot indicates the following points:
- The minimum value (the leftmost point of the whisker)
- The first quartile (Q1, the left edge of the box)
- The median (Q2, the line in the middle of the box)
- The third quartile (Q3, the right edge of the box)
- The maximum value (the rightmost point of the whisker)

Assuming the values you've provided (40, 50, 60, 70, 80) correspond to certain key points in the box-and-whisker plot, let's make some assumptions based on typical distribution:

1. **Assume**:
- Minimum value = 40
- Q1 = 50
- Median = 60
- Q3 = 70
- Maximum value = 80

From this assumption, we can interpret the data distribution as follows:

- **Less than Q1 (50)**: 25% of the data values (this is the lower 25%)
- **Between Q1 (50) and the median (60)**: 25% of the data values (the next 25%)
- **Between the median (60) and Q3 (70)**: 25% of the data values (the next 25%)
- **Greater than Q3 (70)**: 25% of the data values (the upper 25%)

Now, we need to find out how many data values are greater than or equal to 56:

- Data below 56 is:
- Values below Q1 (50), which corresponds to 25% of the data, plus the part of the data between Q1 (50) and the median (60) that is less than 56.
- Since 56 is greater than 50 and less than 60, we can say this range (50 to 60) covers up to 25% of data between the 25% given by Q1.

Thus:
- The percentage below 56:
- Q1 (50): 25%
- Part of Q2 between 50 and 56—a little less than half (let’s assume approximately 12.5% close to this value).

So, *approximately* 37.5% of the data will be less than 56 (25% + approximately 12.5%).

Therefore, calculating the remaining percentage which is more than or equal to 56:
- Total data = 100%
- Data less than 56 = approximately 37.5%

Thus:
- Data greater than or equal to 56 = 100% - approximately 37.5% = **approximately 62.5%.**

**Final answer**: Approximately **62.5%** of the data values are greater than or equal to 56.