8.  A random sample of 10 subjects have weights with a standard deviation of11.7829 kg. What is the variance of their​ weights? Be sure to include the appropriate units with the result. 

The variance of the sample data is _____

 

 9. 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?

39   37   35   28  19   15  13   10   9.6  9.0

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

 

10.  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?

36 45  45  65   70   95   95   170   190   203  260   300  400  1750  2500

The range of the sample data is ____dollars.   ​(Type an integer or a decimal. Do not​ round.)

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

The variance of the sample data is _____dollars squared .

​(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.  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.
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. ​No, there are not any outliers.

 

11.  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.

The range of the data set is ___ degrees F.  ​(Round to two decimal places as​ needed.)

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

The​ variance, s squared​, of the data set is ____ (Round to two decimal places as​ needed.)

 

12  Identify the symbols used for each of the​ following: (a) sample standard​ deviation; (b) population standard​ deviation; (c) sample​ variance; (d) population variance.

1. The symbol for sample standard deviation is ______
2. The symbol for population standard deviation is ______
3. The symbol for sample variance is ______
4. The symbol for population variance is _____

 

13.  Which measure of variation is most sensitive to extreme​ values?  Choose the correct answer below.

1. Range
2. Median
3. Mean
4. Histogram

 

14  Which of the following is NOT a property of the standard​ deviation?Choose the correct answer below.

1. The standard deviation is a measure of variation of all data values from the mean.
2. The value of the standard deviation is never negative.
3. The units of the standard deviation are the same as the units of the original data.
4. When comparing variation in samples with very different​ means, it is good practice to compare the two sample standard deviations.

 

15.  Fill in the blank.  For data sets having a distribution that is approximately​ bell-shaped, _______ states that about​ 68% of all data values fall within one standard deviation from the mean.

 

16. Fill in the blank.  The square of the standard deviation is called the​ _______.

 

17.  A successful basketball player has a height of 6 feet 8​inches, or 203cm. Based on statistics from a data​ set, his height converts to the z score of 4.10.  How many standard deviations is his height above the​ mean?

The​ player’s height is ____ standard​ deviation(s) above the mean.  ​(Round to two decimal places as​ needed.)

 

18.  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 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score.
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 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.
5. 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.

 

19.  Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 74.5Mbps. The complete list of 50 data speeds has a mean of x=18.35Mbps and a standard deviation of s=17.81Mbps.

1. What is the difference between​ carrier’s highest data speed and the mean of all 50 data​ speeds?
2. How many standard deviations is that​ [the difference found in part​ (a)]?
3. Convert the​ carrier’s highest data speed to a z score.
4. If we consider data speeds that convert to z scores between minus2 and 2 to be neither significantly low nor significantly​ high, is the​ carrier’s highest data speed​ significant?

 

1. The difference is ___ Mbps. ​(Type an integer or a decimal. Do not​ round.)
2. The difference is standard deviations. ​(Round to two decimal places as​ needed.)
3. The z score is z=______  ​(Round to two decimal places as​ needed.)
4. The​ carrier’s highest data speed is ___________

 

20.  For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 37 beats per​ minute, the mean of the listed pulse rates is x=79.0 beats per​ minute, and their standard deviation is s=24.6beats per minute.

1. What is the difference between the pulse rate of 37beats per minute and the mean pulse rate of the​ females?
2. How many standard deviations is that​ [the difference found in part​ (a)]?
3. Convert the pulse rate of 37beats per minutes to a z score.
4. If we consider pulse rates that convert to z scores between minus2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 37beats per minute​ significant?

 

1. The difference is _____ beats per minute.
2. The difference is ____ standard deviations. ​(Round to two decimal places as​ needed.)
3. The z score is z=_____​(Round to two decimal places as​ needed.)
4. The lowest pulse rate is ________

 

21.  Consider a value to be significantly low if its z score less than or equal to minus2 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 21.8and the standard deviation was 5.1. 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 between ____ and ______​(Round to one decimal place as needed. Use ascending​ order.)
3. Test scores that are greater than _____​(Round to one decimal place as​ needed.)

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

 

22.  Use z scores to compare the given values.  The tallest living man at one time had a height of 226cm. The shortest living man at that time had a height of 143.9cm. Heights of men at that time had a mean of 177.78cm and a standard deviation of 5.35cm. 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  _______ man had the height that was more extreme.

 

23.  Use z scores to compare the given values.  Based on sample​ data, newborn males have weights with a mean of 3259.4g and a standard deviation of 582.9g. Newborn females have weights with a mean of 3026.6g and a standard deviation of 700.5.  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 _____, the  _____ has the weight that is more extreme.

 

24.  Use z scores to compare the given values.  In a recent awards​ ceremony, the age of the winner for best actor was 32and the age of the winner for best actress was 46. For all best​ actors, the mean age is 45.9 years and the standard deviation is 6.9 years. For all best​ actresses, the mean age is 32.9years and the standard deviation is 12.1years.​ (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.

 

25.   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​ _______.

 

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

 

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

 

28.  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 Q3is _____​cm, and the maximum height is ___ cm

 

29.  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.

The​ 5-number summary is _____________​(Use ascending order. Type integers or decimals. Do not​ round.)

 

Which boxplot below represents the​ data?

 

30.  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.

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?

 

 31.   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.

 

 The​ 5-number summary is ______ all in mBq.

​(Use ascending order. Type integers or decimals. Do not​ round.)

Which boxplot below represents the​ data?

 

32.  Fill in the blank.

In modified​ boxplots, a data value is​ a(n) _______ if it is above Q3 + ​(1.5)(IQR) or below Q1 – ​(1.5)(IQR).

 

33.  Which of the following is NOT a value in the​ 5-number summary?  Choose the correct answer below.

1. Q1
2. Mean
3. Median
4. Minimum