Answer:
The first box and whisker plot
Explanation:
A box and whisker plot gives you the five number summary for a set of data. The five number summary is
- The minimum/lowest value (looks like the top of capital T turned sideways and is the leftmost part of the box-and-whisker plot
- The first quartile or Q1, representing 25% of the data (the first point represented in the "box" of the plot and serves as an endpoint of the box)
- The median or Q2, representing 50%/the middle of the data (the line that splits the box into two parts/the line in the middle of the box)
- The third quartile or Q3, representing 75% of the data (the last point represented in the "box" of the plot and serves as another endpoint of the box)
- The maximum/highest value (also looks like the top of capital T turned sideways and is the rightmost part of the box-and-whisker plot
Maximum and minimum:
We know from the data that the minimum value is 100 and the maximum value is 200. However, because both boxes available as answer choices have the correct minimum and maximum, we'll need to find more data.
Median:
We can start finding the median first by arranging the data from the least to greatest. Then, we find the middle of the data. Because there are 9 points and 9 is odd, we know that there will be 4 points to the left of the median and 4 points to the right of the median:
100, 100, 120, 120, 150, 165, 180, 180, 200
150 has 4 numbers both on its left and right sides so its the median.
Because both of the plots available as answer choices have the correct median, we we'll need to find more data.
First Quartile/Q1:
In order to find Q1, we must find the middle number of the four numbers to the left of the median.
Because we have an even number of points, we will get two middle numbers, 100 and 120. To find the middle of all four points, we average these two numbers:
(100 + 120) / 2 = 220 / 2 = 110
Only the first box has the accurate Q1 value, so it's our answer.
We don't have to find Q3, since both boxes have the correct Q3, but only the first box has the correct minimum, correct Q1, correct median, correct Q3, correct maximum.