Question 1

Given the data set: 10, 13, 27, 19, 11, what is the mean of this 5-point data set?

Accepted Answer

$$\displaystyle \frac{10 + 13 + 27 + 19 + 11}{5} = 16$$

Question 2

For the data set 10, 13, 27, 19, 11, what is the median?

Accepted Answer

$$13$$

Question 3

Suppose you add a sixth value $$x to $$the data set 10, 13, 27, 19, 11 so that the mean of the new 6-point data set is $$1000. $$What must $$x be$$?

Accepted Answer

$$x = 6000 - (10 + 13 + 27 + 19 + 11) = 5920$$

Question 4

If you add a sixth value $$x to $$the data set 10, 13, 27, 19, 11, what value of $$x$$ will make the median of the new data set as large as possible?

Accepted Answer

$$x is $$any value greater than 27$

Question 5

For the data set 10, 13, 27, 19, 11, what value of $$x$$ will make the median of the 6-point data set as small as possible?

Accepted Answer

$$x is $$any value less than 10$

Question 6

Is it possible to choose a value of $$x so $$that the median of the 6-point data set (10, 13, 27, 19, 11, $$x) is$$ $$16$$? If so, what is one such value?

Accepted Answer

No, it is not possible because 16 is not between the two middle values for any arrangement

Question 7

What value of $$x$$ will make the mode of the 6-point data set (10, 13, 27, 19, 11, $$x) as $$large as possible?

Accepted Answer

$$x = 27$$

Question 8

What value of $$x$$ will make the mode of the 6-point data set (10, 13, 27, 19, 11, $$x) as $$small as possible?

Accepted Answer

$$x = 10$$

Question 9

Given the data set 64, 43, 73, 49, 79, 49, 63, what is the mean of this 7-point data set?

Accepted Answer

$$\displaystyle \frac{64 + 43 + 73 + 49 + 79 + 49 + 63}{7} = 60$$

Question 10

What is the median of the 7-point data set: 64, 43, 73, 49, 79, 49, 63?

Accepted Answer

$$49$$

Question 11

Suppose you add an eighth value $$y to $$the data set 64, 43, 73, 49, 79, 49, 63 so that the mean of the new 8-point data set is $$500. $$What must $$y be$$?

Accepted Answer

$$y = 4000 - (64 + 43 + 73 + 49 + 79 + 49 + 63) = 3580$$

Question 12

If you add an eighth value $$y to $$the data set 64, 43, 73, 49, 79, 49, 63, what value of $$y$$ will make the median of the new data set as large as possible?

Accepted Answer

$$y is $$any value greater than 79$

Question 13

What value of $$y$$ will make the median of the 8-point data set (64, 43, 73, 49, 79, 49, 63, $$y) as $$small as possible?

Accepted Answer

$$y is $$any value less than 43$

Question 14

Is it possible to choose a value of $$y so $$that the median of the 8-point data set (64, 43, 73, 49, 79, 49, 63, $$y) is$$ $$57$$? If so, what is one such value?

Accepted Answer

No, it is not possible because 57 cannot be the average of the two middle values for any arrangement

Question 15

What value of $$y$$ will make the mode of the 8-point data set (64, 43, 73, 49, 79, 49, 63, $$y) as $$large as possible?

Accepted Answer

$$y = 79$$

Question 16

What value of $$y$$ will make the mode of the 8-point data set (64, 43, 73, 49, 79, 49, 63, $$y) as $$small as possible?

Accepted Answer

$$y = 43$$

Question 17

A hospital is analyzing patient wait times. If the current wait times are 10, 13, 27, 19, 11 minutes, and a new patient arrives with a wait time of $$x$$ minutes, which value of $$x$$ would most increase the mean wait time?

Accepted Answer

$$x as $$large as possible$

Question 18

A researcher wants to minimize the median value in the data set 64, 43, 73, 49, 79, 49, 63, $$y. $$Which value of $$y$$ should they choose?

Accepted Answer

$$y as $$small as possible$

Step-by-Step Guidance for Statistics Data Set Problems

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