Quiz 2 Chapter 3

 

1.   Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the data and then​ (e) answer the given question. 
Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that​ sport’s league?
188  252  236  194  288  187  289  214   252   211   289
 
 
a. Find the mean. 

The mean is ____ pound(s).  ​(Type an integer or a decimal rounded to one decimal place as​ needed.)

b. Find the median.

The median is ____​pound(s). (Type an integer or a decimal rounded to one decimal place as​ needed.)

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

1. The​ mode(s) is(are) ___________​pound(s).  ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.) 
2. There is no mode.

 

d. Find the midrange.

The midrange is _____ ​pound(s).  (Type an integer or a decimal rounded to one decimal place as​ needed.)

e. Are the results likely to be representative of all players in that​ sport’s league?

1. The results are not likely to be representative because the championship team may not be representative of the entire league. 
2. The results are likely to be representative because a championship team is most likely representative of the entire league.
3. The results are not likely to be representative because the median is not equal to the mean.
4. The results are not likely to be representative because the median is not equal to the mode.

 

2.  Listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. What does this​ “Top 10” list tell us about the population of all of that​ country’s college​ tuitions?
$51,218  $51, 653   $52,267   $52,889   $52,296   $51,218   $53, 831   $52,846   $51, 946   $51,273

Find the​ mean, midrange,​ median, and mode of the data set.

The mean of the data set is _______. ​(Round to two decimal places as​ needed.)

The midrange of the data set is ​________.  ​(Round to two decimal places as​ needed.)

The median of the data set is ​______. ​(Round to two decimal places as​ needed.)

What is​ (are) the​ mode(s) of the data​ set?  Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

1. The​ mode(s) of the data set is​ (are) _____. ​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.) 
2. There is no mode.

 

What does this​ “Top 10” list tell us about the population of all the​ country’s college​ tuitions?

1. All colleges have tuitions around the median. 
2. All colleges have tuitions around the mode.
3. All colleges have tuitions around the mean.
4. All colleges have tuitions around the midrange.
5. Nothing meaningful can be concluded from this information except that these are the largest tuitions of colleges in the country for a recent year.

 

3.  Listed below are pulse rates​ (beats per​ minute) from samples of adult males and females. Find the mean and median for each of the two samples and then compare the two sets of results. Does there appear to be a​ difference?     
     
​Male:
    
56   59  58    88   53   62   53   80   59  92   53   70   55   73   94
​

Female:
    
63   68   95   92   78   66   90  64   91   90   84   95   85   91   83

Find the means. 

The mean for males is ____ beats per minute and the mean for females is ____ beats per minute.  ​(Type integers or decimals rounded to one decimal place as​ needed.)

Find the medians.

The median for males is _____beats per minute and the median for females is _____ beats per minute.  ​(Type integers or decimals rounded to one decimal place as​ needed.)

Compare the results. Choose the correct answer below.

1. The mean and the median for males are both lower than the mean and the median for females.
2. The mean and the median for females are both lower than the mean and the median for males.
3. The mean and median appear to be roughly the same for both genders.
4. The mean is lower for​ males, but the median is lower for females.
5. The median is lower for​ males, but the mean is lower for females.

 

Does there appear to be a​ difference?

1.  The pulse rates for males appear to be higher than the pulse rates for females.
2. Since the sample size is​ small, no meaningful information can be gained from analyzing the data.
3. There does not appear to be any difference.
4. The pulse rates for females appear to be higher than the pulse rates for males.

 

4.  One common system for computing a grade point average​ (GPA) assigns 4 points to an​ A, 3 points to a​ B, 2 points to a​ C, 1 point to a​ D, and 0 points to an F. What is the GPA of a student who gets an A in a 4 ​-credit ​course, a B in each of three 3​-credit ​courses, a C in a 4​-credit ​course, and a D in a 3​-credit ​course?

The mean grade point score is ______

 

5. A​ student’s course grade is based on one midterm that counts as 5​% of his final​ grade, one class project that counts as 15​% of his final​ grade, a set of homework assignments that counts as 40​%  of his final​ grade, and a final exam that counts as 40​% of his final grade. His midterm score is 81​, his project score is 96, his homework score is 88​, and his final exam score is 80. What is his overall final​ score? What letter grade did he earn​ (A, B,​ C, D, or​ F)? Assume that a mean of 90 or above is an​ A, a mean of at least 80 but less than 90 is a​ B, and so on.

His overall final score is _____

 

His letter grade is ______

 

6.  Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​ salaries, do we know anything about the variation of salaries of TV personalities in​ general?

38  37   36   30   18    14    13    9   8.8    8.3
 
The range of the sample data is ​______ million. ​(Type an integer or a​ decimal.)

The variance of the sample data is ______.  ​(Round to two decimal places as​ needed.)

The standard deviation of the sample data is ​______million.  ​(Round to two decimal places as​ needed.)

Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in​ general?

1. No, because the sample is not representative of the whole population. 
2. ​Yes, because the standard deviation is an unbiased estimator. 
3. ​No, because there is an outlier in the sample data. 
4. ​Yes, because the sample is random.

 

7.   Listed below are the amounts​ (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any​ outliers, and are they likely to have much of an effect on the measures of​ variation?
38  50   50  55   65    85    95   150   175   218   250    325   450  1750  3000
 
The range of the sample data is ______.  ​(Type an integer or a decimal. Do not​ round.)

The standard deviation of the sample data is ______ ​(Round to one decimal place as​ needed.)

The variance of the sample data is _______ ​(Round to one decimal place as​ needed.)

Are there any outliers​ and, if​ so, are they likely to have much of an effect on the measures of​ variation?

1. ​No, there are not any outliers.
2. Yes, the largest amounts are much higher than the rest of the​ data, and appear to be outliers. It is not likely that these are having a large effect on the measures of variation.
3. ​Yes, the largest amounts are much higher than the rest of the​ data, and appear to be outliers. It is likely that these are having a large effect on the measures of variation.
4. ​Yes, the smallest amounts are much lower than the rest of the​ data, and appear to be outliers. It is not likely that these are having a large effect on the measures of variation.

 

 

8.   Use software or a calculator to find the​ range, variance, and standard deviation of the following body​ temperatures, in degrees​ Fahrenheit, taken at​ 12:00 A.M.

Data Table

The range of the data set is ______.  Round to two decimal places as​ needed.)

The standard​ deviation, s, of the data set is ______ ​(Round to two decimal places as​ needed.)

The​ variance,

$s^2$

​,  of the data set is _____​(Round to two decimal places as​ needed.)

 

 

9.  A successful basketball player has a height of 6 feet 10​inches, or 208cm. Based on statistics from a data​ set, his height converts to the z score of 4.81.   How many standard deviations is his height above the​ mean?

The​ player’s height is _____ standard​ deviation(s) above the mean. 

 

10.  The boxplot shown below results from the heights​ (cm) of males listed in a data set. What do the numbers in that boxplot tell​ us?

The minimum height is _____ ​cm, the first quartile Q1 is _____ ​cm, the second quartile Q2  ​(or the​ median) is _____  cm,  the third quartile Q3 is _____ cm, and the maximum height is _____ cm.

 

11.   If your score on your next statistics test is converted to a z​ score, which of these z scores would you​ prefer: -2.00, -1.00, 0, 1.00, 2.00? Why?

1. The z score of 0 is most preferable because it corresponds to a test score equal to the mean.
2. The z score of -2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. 
3. The z score of -1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score.
4. The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score.
5. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. 

 

12.  Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 72.5Mbps. The complete list of 50 data speeds has a mean of

$\overline{x}=$

15.14 Mbps and a standard deviation of s=19.35Mbps.
a. What is the difference between​ carrier’s highest data speed and the mean of all 50 data​ speeds?
b. How many standard deviations is that​ [the difference found in part​ (a)]?
c. Convert the​ carrier’s highest data speed to a z score.
d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the​ carrier’s highest data speed​ significant?

a. The difference is _____ Mbps.  ​(Type an integer or a decimal. Do not​ round.)

b. The difference is _____ standard deviations.  ​(Round to two decimal places as​ needed.)

c. The z score is z= _______ (Round to two decimal places as​ needed.)

d. The​ carrier’s highest data speed is ____________________ 

 

13.  For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 31 beats per​ minute, the mean of the listed pulse rates is

$\overline{x}$

= 79.0 beats per​ minute, and their standard deviation is s = 15.4 beats per minute.

a. What is the difference between the pulse rate of 31 beats per minute and the mean pulse rate of the​ females?
b. How many standard deviations is that​ [the difference found in part​ (a)]?
c. Convert the pulse rate of 31 beats per minutes to a z score.
d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 31 beats per minute​ significant?

a. The difference is ____________ beats per minute.  ​(Type an integer or a decimal. Do not​ round.)

b. The difference is ________ standard deviations.  ​(Round to two decimal places as​ needed.)

c. The z score is z = _______ ​(Round to two decimal places as​ needed.)

d. The lowest pulse rate is  ________________

 

 

14.   Consider a value to be significantly low if its z score less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A test is used to assess readiness for college. In a recent​ year, the mean test score was 20.7 and the standard deviation was 4.9.  Identify the test scores that are significantly low or significantly high. 

What test scores are significantly​ low? Select the correct answer below and fill in the answer​ box(es) to complete your choice.

1. Test scores that are less than _____. ​(Round to one decimal place as​ needed.) 
2. Test scores that are greater than _______​(Round to one decimal place as​ needed.)
3. Test scores that are between ________ and and _____ ​(Round to one decimal place as needed. Use ascending​ order.)

 

What test scores are significantly​ high? Select the correct answer below and fill in the answer​ box(es) to complete your choice.

1. Test scores that are greater than ______​(Round to one decimal place as​ needed.)
2. Test scores that are between _____ and ______ ​(Round to one decimal place as needed. Use ascending​ order.)
3. Test scores that are less than __________​(Round to one decimal place as​ needed.)

 

15.  Use z scores to compare the given values.  The tallest living man at one time had a height of 236cm. The shortest living man at that time had a height of 77.7cm. Heights of men at that time had a mean of 170.14cm and a standard deviation of 7.32cm. Which of these two men had the height that was more​ extreme?

Since the z score for the tallest man is z = _____ and the z score for the shortest man is z = _____, the ___________ shortest man had the height that was more extreme.
​(Round to two decimal​ places.)

 

16  Use z scores to compare the given values.  Based on sample​ data, newborn males have weights with a mean of 3247.4g and a standard deviation of 589.6g. Newborn females have weights with a mean of 3089.9g and a standard deviation of 655.5g. Who has the weight that is more extreme relative to the group from which they​ came: a male who weighs 1600g or a female who weighs 1600​g?

Since the z score for the male is z = _______ and the z score for the female is z = _______ , the ____ has the weight that is more extreme.  ​(Round to two decimal​ places.)

 

17. Use z scores to compare the given values. In a recent awards​ ceremony, the age of the winner for best actor was 32 and the age of the winner for best actress was 50.  For all best​ actors, the mean age is 43.3 years and the standard deviation is 5.8 years. For all best​ actresses, the mean age is 36.9 years and the standard deviation is 11.4 
years.​ (All ages are determined at the time of the awards​ ceremony.) Relative to their​ genders, who had the more extreme age when winning the​ award, the actor or the​ actress? Explain.

Since the z score for the actor is z = _____ and the z score for the actress is z = ____ , the  _______ had the more extreme age.  ​(Round to two decimal​ places.)

 

 

18.  The following are the ratings of males by females in an experiment involving speed dating. Use the given data to construct a boxplot and identify the​ 5-number summary.
2.0   2.5   3.0   3.5   4.5  4.5   5.5   5.5    5.5   5.5   5.5   6.5   7.5   7.5   7.5   7.5   8.0   8.5   8.5   9.5  
 
The​ 5-number summary is ___,   ___, ____,   _____, and ____.  ​(Use ascending order. Type integers or decimals. Do not​ round.)

Which boxplot below represents the​ data?

 

 

19. Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to 11 cell phones. Use the given data to construct a boxplot and identify the​ 5-number summary.
1.49  0.86   0.87   0.76    1.14    1.13    1.37   0.72    1.48   0.52    1.09       

The​ 5-number summary is ___, ____, ____,   ____, _____ all in​ W/kg.  ​(Use ascending order. Type integers or decimals. Do not​ round.)

Which boxplot below represents the​ data?

 

 20. Listed below are amounts of​ strontium-90 (in​ millibecquerels, or​ mBq) in a simple random sample of baby teeth obtained from residents in a region born after 1979. Use the given data to construct a boxplot and identify the​ 5-number summary.
122  123  127  131  132  136   136  137  141  144
 
148   149   150    151   153   160   162   164   168  174

The​ 5-number summary is ___,  ____, ___,  ____, ____  all in mBq.  ​(Use ascending order. Type integers or decimals. Do not​ round.)

Which boxplot below represents the​ data?

 

21.   Fill in the blank.
When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the​ mean, we call the new value a​ _______.

 

22.  Fill in the blank.  A data value is considered​ _______ if its​ z-score is less than -2 or greater than 2.

 

23.   Fill in the blank.  Whenever a data value is less than the​ mean, _______.

 

24.  Fill in the blank.  In modified​ boxplots, a data value is​ a(n) _______ if it is above

$Q_3$

+ ​(1.5)(IQR)  or below

$Q_1$

– ​(1.5)(IQR).