By using the above figure, we are asked if the value 11 is always contained in the data set. The rightmost point on a box-and-whisker plot represents the greatest value of the data set, which is 11. This means that the value is contained in the data set. Therefore, the statement is always true.
b In this part, we are asked if the value 6 is always in the data set. Let's first note that the given box-and-whisker plot could represent the following data set.
2, 4,5, 5,5, 8,11
As we can see, the value 6 is not contained in the data set. Since we have an example of a data set that meets all the requirements but does not contain the value 6, the statement is not always true.
c In this part, we are asked if the data set is always skewed right. Note that the right whisker is longer than the left whisker, and most of the data are on the left side of the plot. Therefore, the statement is always true.
d In this part, we are asked if the mean of the data is always 5. Let's calculate the mean of the data set we used in Part B.
x=2+4+5+5+5+8+11/7 ⇓ x≈ 5.71
As we can see, the mean is different than 5. Since we have an example of a data set that meets all the requirements but does not have a mean of 5, the statement is not always true.
