Answer:
B
Step-by-step explanation:
Definitions
Minimum is the smallest value in the data set, while maximum is the largest value.
Median is the number in the middle of the data set when the data is arranged in ascending order.
Identifying minimum, maximum and median
Minimum= 3
Maximum= 18
Median= 10
The median can be found by taking the value of the (n+1)/2 number in a data set of n numbers.
In this case, each of the data sets in the options have 11 numbers. Thus, the median number is the 6th number when the numbers are arranged in ascending order.
Identifying the correct data set
Minimum and maximum are the easiest to identify so let's start by identifying those in each option. In options A to C, the minimum and maximum are 3 and 18 respectively. This is in line with what we have identified from the box and whisker plot. However, option D is eliminated as the minimum is 2 instead of 3.
Next we can identify the median by looking at the 6th number in each option.
Option A: median= 12 (incorrect)
Option B: median= 10
Option C: median= 10
Using the median, option A is eliminated too.
Let's look at the box and whisker plot again. The left end of the box is the lower quartile, which is the 25% mark of the data set.
Lower quartile= ¼(n +1), where n is the number of values in the data set
Lower quartile
= (11 +1) ÷4
= 12 ÷4
= 3
Lower quartile is the 3rd value of the data set (when it is arranged in ascending order). From the box and whisker plot, the lower quartile is 7.
The lower quartile of option B is 7, while that of C is 8. Thus, option B is the correct answer.
Note:
• Instead of using lower quartile, you could also use upper quartile which is the right end of the box in the box and whisker plot.
Upper quartile= ¾(n +1)
• The box is the rectangle in the plot, while the whiskers are the straight lines that extends from the box. The whiskers includes the minimum/ maximum point.
