Question

Which of the following dot plots correctly represents the given information?
● The median of the data is 71.
● The lower quartile is 70.
● The upper quartile is 73.

Figure 1:

Figure 2:

• A. Figures 1 and 2 are the correct representations.
• B. Figure 1 is the correct representation
• C. Figure 2 is the correct representation.
• D. None of the figures correctly represent the given information.

Answer 1

The correct option is D None of the figures correctly represent the given information.

For figure 1:
The ordered data set is: 68, 69, 70, 70, 71, 71, 71, 71, 72, 72, 72, 73, 73, 74, 74, 75
We can observe that the data has 16 values. Therefore, the median will be $\frac{71+72}{2}=71.5$.
We can also say that the median is not 71, but 71.5. So the data is not represented by figure 1.

For figure 2:
The ordered data set is: 60, 64, 64, 66, 66, 68, 68, 70, 70, 70, 70, 72, 72, 72, 74, 74, 76, 76, 76, 76, 76, 80
We can observe that the data has 22 values, so the median will be $\frac{70+72}{2}=71$.

We can say that the median is 71.
Let's check the lower quartile for the first half of the data set, i.e., 60, 64, 64, 66, 66, 68, 68, 70, 70, 70, 70. So, the lower quartile is 68 not 70, which is not true for figure 2.

Hence, we can say that the given data does not match any of the given figures.