To answer the question for each measure, let's consider a random box-and-whisker plot. This plot consists of five numbers — the minimum, the first quartile (Q_1), the median (Q_2), the third quartile (Q_3), and the maximum of a data set.
To find the mean of data, we need to know all of the data values. When a box-and-whisker plot is given, we can only determine some of the values — for example, the minimum and maximum values. Therefore, it is not possible to find the mean when given only the box-and-whisker plot.
Measure
Definition
Can Be Found on a Box-and-Whisker Plot?
Mean
The sum of data values divided by the total number of data values
No *
Median
The middle value in an ordered data set
?
Mode
The data item that occurs the most times
?
Let's now consider the median. Recall that the vertical line in the box represents the median. Therefore, the median can be found looking at the box-and-whisker plot.
Measure
Definition
Can Be Found on a Box-and-Whisker Plot?
Mean
The sum of data values divided by the total number of data values
No *
Median
The middle value in an ordered data set
Yes ✓
Mode
The data item that occurs the most times
?
Finally, the mode is used to find the most popular value in a data set. Similar to the mean, all of the data values must be known to determine which values occur the most times. Because of this, we cannot find the mode by looking only at a box-and-whisker plot.
Measure
Definition
Can Be Found on a Box-and-Whisker Plot?
Mean
The sum of data values divided by the total number of data values
