Question 1

The mode and the mean for the same set of data can be equal.

Accepted Answer

The mode and the mean of a data set can be equal, especially in symmetric distributions where values are evenly spread around a central value.

Question 2

Suppose that the class mean on a test is 81.2%. What does the 81.2% mean (not how it was calculated)?

Accepted Answer

The answer of Suppose that the class mean on a...

Question 3

Calculate the standard deviation for these scores: 80, 72, 80, and 88. Show your work for credit.

Accepted Answer

The answer of Calculate the standard deviation for these scores:...

Question 4

The standard deviations for the test scores for two classes are quite different (on the same test). What does that tell you?

Accepted Answer

The answer of The standard deviations for the test scores...

Question 5

The mean scores for two classes are quite different. Does that imply that the standard deviation for the class with the larger mean will be greater than the standard deviation for the other class? Explain.

Accepted Answer

The answer of The mean scores for two classes are...

Question 6

The median, rather than the mean or mode, is often given in reports about house prices. Why is that?

Accepted Answer

The answer of The median, rather than the mean or...

Question 7

Sketch two distributions that would have the same median but different standard deviations.

Accepted Answer

The answer of Sketch two distributions that would have the...

Question 8

A) For what kind of distribution does the 68-95-99.7 rule work?
B) What is the 68-95-99.7 rule or summary? If it helps your explanation, use a drawing.
C) One year, the SAT verbal test had scores with a mean of 500 and a standard deviation of 100. SAT scores are normally distributed. Approximately what percent of the people taking the SAT verbal test that year scored above 600? (Write or draw enough to make your reasoning clear.)

Accepted Answer

The answer of A) For what kind of distribution does...

Question 9

A particular medicine is not effective if there is less than 147 milligrams of Xylz in a dose, and the medicine is dangerous if there is more than 153 milligrams of Xylz in a dose. One manufacturer of the medicine uses a process that gives medicine with a normally distributed strength of Xylz, with mean 150 milligrams and standard deviation 1.5 milligrams of Xylz per dose. Approximately what percent of the manufacturer's total production will be thrown out and not used because of effectiveness or safety reasons?

Accepted Answer

The answer of A particular medicine is not effective if...

Question 10

Aña took both the SAT and the ACT before going to college. Her SAT verbal test had a mean of 500 and a standard deviation of 100. Aña's score was 620. Her ACT had a mean of 18 and a standard deviation of 6. Aña's score was 26. On which test did Aña do better compared with the others who took the tests?

Accepted Answer

The answer of Aña took both the SAT and the...

Question 11

A study at the public library in Highbrow City indicated that the number of visitors per week had a mean of 850 and a standard deviation of 70. A similar study at the public library in Podunk Township indicated that the number of visitors per week had a mean of 730 and a standard deviation of 50. In a contest during library week, the Highbrow City library attracted 990 people, while the library in Podunk Township attracted 840. Highbrow said they won because they not only had more people than Podunk, but they also had 140 extra people above the mean, while Podunk had only 110 extra people above their mean. How should Podunk respond?

Accepted Answer

The answer of A study at the public library in...

Question 12

In a normal distribution, at what percentile is each of these z-scores? 
A) $z = 3$
B) $z = 0$
C) $z = - 2$

Accepted Answer

The answer of In a normal distribution, at what percentile...

Quiz 30: Representing and Interpreting Data With One Variable