Homework 6

1.What does it mean if a statistic is​ resistant?  Choose the correct answer below.

1. An estimate of its value is extremely close to its actual value.
2. Changing particular data values affects its value substantially.
3. Extreme values​ (very large or​ small) relative to the data do not affect its value substantially.
4. Extreme values​ (very large or​ small) relative to the data affect its value substantially.

 

2.   A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why?  Choose the correct answer below.

1. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail.
2. The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.
3. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail.
4. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail.

 

3.   Why is the median​ resistant, but the mean is​ not?  Choose the correct answer below.

1. The mean is not resistant because it is dependent upon the sample​ size, n. The larger n​ is, the smaller the mean becomes.​ However, the median is resistant because it is not dependent on the sample​ size, n.
2. The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which do not pull the mean in that direction.​ However, the median is pulled in the direction of the extreme​ values, making it resistant.
3. The median is​ resistant, while the mean is​ not, because when there are extreme values in the​ tail, the value of the median changes while the mean does not.
4. The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.

 

4.  When an observation that is much larger than the rest of the data is added to a data​ set, the value of the mean will​ __________________.

 

5.  Determine if the statement is true or false.  When an observation that is much larger than the rest of the data is added to a data​ set, the value of the median will increase substantially.  Choose the correct answer below.

1. True
2. False

 

6.  For a distribution that is​ symmetric, which of the following is​ true?  Choose the correct answer below.

1. mean<median
2. mean=median
3. mean>median

 

7. For a distribution that is skewed​ right, which of the following is​ true? Choose the correct answer below.

1. mean<median
2. mean=median
3. mean>median

 

8.   For a distribution that is skewed​ left, which of the following is​ true?  Choose the correct answer below.

1. mean<median
2. mean=median
3. mean>median

 

9.  The U.S. Department of Housing and Urban Development​ (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the​ median?  Choose the correct answer below.

1. HUD uses the median because the data are skewed right.
2. HUD uses the median because the data are skewed left.
3. HUD uses the median because the data are bimodal.
4. HUD uses the median because the data are symmetrical.

 

10.   The histogram on the right represents the connection time in seconds to an internet provider. Determine which measure of central tendency better describes the​ “center” of the distribution.

What measure of central tendency best describes the​ “center” of the​ distribution?

1. Mean
2. Median
3. Mode

 

11.  In​ 1994, major league baseball players went on strike. At the​ time, the average salary was​ $1,049,589, and the median salary was​ $337,500. If you were representing the​ owners, which summary would you use to convince the public that a strike was not​ needed? If you were a​ player, which would you​ use? Why was there such a large discrepancy between the mean and median​ salaries? Explain.

Select the correct answers below.

If you were representing the​ owners, you would use the _____ to convince the public that a strike was not needed. If you were a​ player, you would use the _______ to convince the public that a strike was needed. The average and median salaries differ so greatly because the distribution of salaries is skewed right.

 

12.  For the distribution​ shown, match the letter to the measure of central tendency.

Drag each of the letters into the appropriate measure of central tendency.

C –

B –

A –

 

13.  True or​ False: A data set will always have exactly one mode.

Choose the correct answer below.

1. False
2. True

 

14  A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The following data represent the strength of nine randomly selected casts​ (in psi).

3970​, 4080​, 3200​, 3000​, 2940​, 3820​, 4080 ​, 4040​, 3720

Compute the mode strength of the concrete​ (in psi).

Compute the mode strength of the concrete. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The mode of the strengths of the concrete is psi of pressure.​(Round to the nearest tenth as​ needed.)
2. The mode does not exist.

 

15.  A sample of 20 registered voters was surveyed in which the respondents were​ asked, “Do you think​ Chang, Johnson,​ Ohm, or Smith is most qualified to be a​ senator?” The results of the survey are shown in the table.

Complete parts​ (a) and​ (b) to the right.

​(a) Determine the mode candidate.

1. Smith
2. Johnson
3. Ohm
4. Chang

​(b) Do you think it would be a good idea to rotate the candidate choices in the​ question? Why?

1. ​Yes, to make the resulting counts all closer to each other
2. ​Yes, to confuse the respondents
3. ​Yes, to avoid response bias
4. There is no need to rotate the choices.

 

16. A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The following data represent the strength of nine randomly selected casts​ (in psi).

3970​, 4090​, 3300​, 3100​, 2950​, 3840​, 4090​, 4030​, 3750

Compute the mode strength of the concrete​ (in psi).

Compute the mode strength of the concrete. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The mode of the strengths of the concrete is psi of pressure.  ​(Round to the nearest tenth as​ needed.)
2. The mode does not exist.

 

17.  Find the population mean or sample mean as indicated.

​Sample:

21​, 18​, 4​, 6​, 11

Select the correct choice below and fill in the answer box to complete your choice.

1. $\chi =12$
2. $\mu =\_\_\_$

 

 

18  Find the population mean or sample mean as indicated.

​Population:

4​, 8​, 10​, 15​, 8

Select the correct choice below and fill in the answer box to complete your choice.

 

19.  For a large sporting event the broadcasters sold 53 ad slots for a total revenue of ​$176 million. What was the mean price per ad​ slot?

The mean price per ad slot was _____ million

 

20.  Mr. Zuro finds the mean height of all 13students in his statistics class to be 69.0 inches. Just as Mr. Zuro finishes explaining how to get the​ mean, Danielle walks in late. Danielle is 70.4 inches tall. What is the mean height of the 14 students in the​ class?

The mean height of the 14students in the class is _____ inches

 

21.  A professor has recorded exam grades for 30 students in his​ class, but one of the grades is no longer readable. If the mean score on the exam was 82 and the mean of the 29 readable scores is 84​, what is the value of the unreadable​ score?

The value of the unreadable score is _______

 

22.   The median for the given set of six ordered data values is 27.5.

9 12, 23,​ 41, 48

What is the missing​ value?  The missing value is ____

 

23  A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The following data represent the strength of nine randomly selected casts​ (in psi).

3950​, 4080​, 3200​, 3000​, 2930​, 3830​, 4080​, 4050​, 3730 

Compute the median strength of the concrete​ (in psi).

The median strength of the concrete is ____ psi of pressure

 

24.  The following data represent the monthly cell phone bill for a​ person’s phone for six randomly selected months.

​$35.34​, ​$42.09​, $39.47​, ​$38.87​, ​$43.39​, ​$49.26  Compute the median phone bill.

The median phone bill is ______.

​(Round to the nearest cent as​ needed.)

 

25.   An insurance company crashed four cars of the same model at 5 miles per hour. The costs of repair for each of the four crashes were ​$410​, ​$413​, ​$454​, and ​$219  .   Compute the​ mean, median, and mode cost of repair.

Compute the mean cost of repair. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The mean cost of repair is ____.  ​(Round to the nearest cent as​ needed.)
2. The mean does not exist.

 

Compute the median cost of repair. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The median cost of repair is ____ .  ​(Round to the nearest cent as​ needed.)
2. The median does not exist.

Compute the mode cost of repair. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The mode cost of repair is ____. ​(Round to the nearest cent as​ needed.)
2. The mode does not exist.

 

26.   A certain type of concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The concrete is poured into casting cylinders and allowed to set for 28 days. The​ concrete’s strength is then measured. The following data represent the strength of nine randomly selected casts​ (in psi). Compute the​ mean, median, and mode strength of the concrete​ (in psi).

3920 4060 3220 3120 2930 3870 4060 4080 3780

Compute the mean strength. Select the correct choice below and fill in the answer box to complete your choice.

1. The mean strength is _____ ​(Round to two decimal places as​ needed.)
2. The mean does not exist.

 

Compute the median strength. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The median strength is ____ ​(Round to two decimal places as​ needed.)
2. The median does not exist.

 

Compute the mode strength. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The mode strength is _____ ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)
2. The mode does not exist.

 

27.