The mean of plot B is greater than the mean of plot A. (Option A), and The interquartile range of plot B is the same as the interquartile range of plot A. (Option D)
How does a boxplot shows the data points?
A box plot has 5 data description.
- The leftmost whisker shows the minimum value in the data.
- The rightmost whisker shows the maximum value in the data.
- The leftmost line in the box shows the first quartile.
- The middle line shows the median, also called second quartile.
- The last line of the box shows the third quartile.
How to find the interquartile range?
IQR(inter quartile range) is the dfference between third and first quartile.
What is the range of a data set?
Range = Maximum value of the data set - Minimum value of the dataset
For first box plot: (Plot A)
- Minimum = 4
- First quartile = 5
- Second quartile = Median = 7
- Third quartile = 9
- Maximum value = 10
Range = max - min = 10 - 4 = 6
IQR = third quartile - first quartile = 9 - 5 = 4
Due to symmetry, mean = meadian = mode, therefore, mean = median = 7 = mode.
For second box plot: (Plot B)
- Minimum = 8
- First quartile = 9
- Second quartile = Median = 11
- Third quartile = 13
- Maximum value = 14
Range = max - min = 14 - 8 = 6
IQR = third quartile - first quartile = 13 - 9 = 4
Due to symmetry, mean = meadian = mode, therefore, mean = median = 11 = mode.
So, we see that the mean and median of first plot (plot A) is smaller than t he mean and median of plot B.
Thus, Option A. The mean of plot B is greater than the mean of plot A. is correct option.
and Option D. The interquartile range of plot B is the same as the interquartile range of plot A. is correct option
Option B and C are wrong, as range is same for both plot, and the median of both plots aren't same.
Thus, the mean of plot B is greater than the mean of plot A. (Option A), and The interquartile range of plot B is the same as the interquartile range of plot A. (Option D) are the only correct options.
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