Given the set of data:
5, 4, 16, 21, 10, 6, 15
Let's create a box-and-whisker plot from the given data.
The box and whisker plot has the following properties:
Let's solve for the following:
• Minimum value or lower extreme:
This is the smallest value in the data set.
Here, the minimum value is 4.
• Maximum value or upper extreme:
This is the greatest number in the data set.
Here, the greatest number is 21.
• Median:
This is the middle value after arranging the data in ascending order(from lowest to greatest).
Arranging in ascending order, we have:
4, 5, 6, 10, 15, 16, 21
The middle number above is = 10
Therefore the median is 10.
• Lower quartile:
The lower quartile is the median of the lower half of the data.
To find the lower quartile, let's list the lower half of data first.
Lower half:
4, 5, 6
The median of the lower half of the data is 5.
Therefore, the lower quartile is 5.
• Upper quartile:
The upper quartile is the median of the upper half of the data set.
Upper half of the data set:
15, 16, 21
The median is 16.
The upper quartile is 16.
Therefore the box and whisker plot created from the given data set is:
Option B is correct.
ANSWER:
B