We have 15 data points.
1, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 11
Let's find the median. (The one in the middle)
Just count by one from each side until they meet in the middle.
The median is 6.
This is represented in the box-and-whisker plot as the line that splits the box. We know that line has to go over 6.
The lowest and highest numbers, or extremes, (1 and 11) should be the dots.
These things might have helped us to make a box-and-whisker plot, but all of our answers have these, so we're out of luck.
The ends of the box should be at what are called quartiles.
The median between the lower extreme (1) and our big median (the second 6) is called our lower quartile.
We find this in the same way that we did the median, by counting in.
Remember to start at your lower extreme on one end but just below the median on the other end.
You will find that the lower quartile is 5.
The median between the upper extreme (11) and our big median (the second 6) is called our upper quartile.
Same way as the first two times, count inwards.
One finger on the upper extreme, and the other just above the median.
And our upper quartile, as you will find, is 8.
Now we just need to look for the box-and-whisker plot with quartiles 5 and 8. (remember, these are the ends of the box)
The correct answer is D.
Extra info:
Alternate names for things:
lower extreme = minimum
upper extreme = maximum
lower quartile = first quartile
upper quartile = third quartile
also: the amount between the extremes is the range.
the amount between the quartiles is the interquartile range.
