the box - and - whisker plot below represents some data set. what percentage of the data values are greater…

Explanation:

Step1: Identify quartile values

In a box - and - whisker plot, the box represents the inter - quartile range (IQR). The left - hand side of the box is the first quartile ($Q_1$), the line inside the box is the median ($Q_2$), and the right - hand side of the box is the third quartile ($Q_3$). Here, assume the values are evenly spaced on the number line. The box starts around 40 and ends around 60. The value 56 is between $Q_1$ (40) and $Q_3$ (60).

Step2: Recall quartile percentages

The first quartile ($Q_1$) represents the 25th percentile, the median ($Q_2$) represents the 50th percentile, and the third quartile ($Q_3$) represents the 75th percentile.

Step3: Calculate the percentage

Since 56 is greater than the median (50th percentile) and less than $Q_3$ (75th percentile), we know that 50% of the data is less than or equal to the median and 25% of the data is between the median and $Q_3$. To find the percentage of data greater than or equal to 56, we note that the data from the median to the maximum value is 50% of the data. Since 56 is in the second half of the data (above the median), and it is closer to the median than $Q_3$, we calculate as follows. The distance from the median to 56 is a fraction of the distance from the median to $Q_3$. But since we know that the data above the median is 50%, and 56 is in the lower part of the upper - half of the data, we can estimate. The value 56 is 16 units above the median (assuming the median is 40) and the distance from the median to $Q_3$ (60) is 20 units. The proportion of the upper - half of the data that is less than 56 is $\frac{16}{20}= 0.8$. So the proportion of the upper - half of the data that is greater than or equal to 56 is $1 - 0.8=0.2$. The total percentage of data greater than or equal to 56 is $50+(0.2\times50)= 30%$.

Answer:

30%