#1

Find the(a) mean,(b) median,(c) mode, and(d) midrange for the data and then(e) answer the given questions.

Listed below are the highest amounts of net worth(in millions ofdollars) of all celebrities. What do the results tell us about the population of allcelebrities? Based on the nature of theamounts, what can be inferred about theirprecision?

260200195180170170165165165165

a. Find the mean.

The mean is $______million.

(Type an integer or a decimal rounded to one decimal place asneeded.)

b. Find the median.

The median is $______million.

(Type an integer or a decimal rounded to one decimal place asneeded.)

c. Find the mode.

Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A.

Themode(s) is(are) $______million.

(Type an integer or a decimal. Do not round. Use a comma to separate answers asneeded.)

B. There is no mode.

d. Find the midrange.

The midrange is $______million.

(Type an integer or a decimal rounded to one decimal place asneeded.)

e. What do the results tell us about the population of allcelebrities?

A.

Apart from the fact that all other celebrities have amounts of net worth lower than thosegiven, nothing meaningful can be known about the population.

B.

The results tell us that the most common celebrity net worth is themode, but all other celebrities are expected to have net worths approximately equal to themean, median, or midrange.

C.

The results tell us that all celebrities are expected to have amounts of net worth approximately equal to one of the measures of center found in parts(a) through(d).

D.

Apart from the fact that all other celebrities have amounts of net worth lower than thosegiven, the results in parts(a), (b), and(d) do not given meaningful results.However, the result from part(c) shows that the most common celebrity net worth is equal to the mode.

Based on the nature of theamounts, what can be inferred about theirprecision?

A.

The values are all wholenumbers, so they appear to be accurate to the nearest whole number.

B.

Since celebrity information ispublic, these values can be assumed to be unrounded.

C.

Since no information isgiven, nothing can be said about the precision of the given values.

D.

The values all end in 0 or5, so they appear to be rounded estimates.

#2

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 57.6 degrees.

Low Temperature (F) 4044 4549 5054 5559 6064

Frequency 2 7 9 7 2

The mean of the frequency distribution is _____degrees.

(Round to the nearest tenth asneeded.)

Which of the following best describes the relationship between the computed mean and the actualmean?

A.

The computed mean is close to the actual mean because the difference between the means is less than5% of the actual mean.

B.

The computed mean is close to the actual mean because the difference between the means is more than5% of the actual mean.

C.

The computed mean isnot close to the actual mean because the difference between the means is less than5% of the actual mean.

D.

The computed mean isnot close to the actual mean because the difference between the means is more than5% of the actual mean.

#3

Because the mean is very sensitive to extremevalues, it is not a resistant measure of center. By deleting some low values and highvalues, the trimmed mean is more resistant. To find the10% trimmed mean for a dataset, first arrange the data inorder, then delete the bottom10% of the values and delete the top10% of thevalues, then calculate the mean of the remaining values. Use the axial loads(pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify anyoutliers, then compare themedian, mean,10% trimmedmean, and20% trimmed mean.

247 261 269 274 275 278 282 282 283 285

285 289 290 290 294 295 297 298 308 505

Identify any outliers. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A.

Theoutlier(s) is/are ______pounds.

(Type a whole number. Use a comma to separate answers asneeded.)

B.

There are no outliers.

The median is ______pounds.

(Type an integer or decimal rounded to one decimal place asneeded.)

The untrimmed mean is ______pounds.

(Type an integer or decimal rounded to one decimal place asneeded.)

The10% trimmed mean is ______pounds.

(Type an integer or decimal rounded to one decimal place asneeded.)

The20% trimmed mean is ______pounds.

(Type an integer or decimal rounded to one decimal place asneeded.)

Compare the values. Choose the correct answer below.

A.

Themedian, 10% trimmedmean, and20% trimmed mean are close to each other.However, the untrimmed mean is significantly different from those values.

B.

Themedian, untrimmedmean, and20% trimmed mean are close to each other.However, the10% trimmed mean is significantly different from those values.

C.

The untrimmedmean, 10% trimmedmean, and20% trimmed mean are close to each other.However, the median is significantly different from those values.

D.

All of the values are close to each other.

E.

Themedian, untrimmedmean, and10% trimmed mean are close to each other.However, the20% trimmed mean is significantly different from those values.

#5

The brain volumes (cm3) of 20 brains have a mean of 1099.6 cm3 and a standard deviation of 127.3 cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For suchdata, would a brain volume of 1364.2 cm3 be significantlyhigh?

Significantly low values are _____cm³ or lower.

(Type an integer or a decimal. Do notround.)

Significantly high values are _______cm³ or higher.

(Type an integer or a decimal. Do notround.)

Is 1364.2 cm³ significantlyhigh?

A.

Yes,becauseitisbelowthelowerlimitseparatingvalue.

B.

No, because it is above the upper limit separating value.

C.

Yes,becauseitisabovetheupperlimitseparatingvalue.

D.

No, because it is below the lower limit separating value.

E.

No,becauseitisbetweenthelimitsseparatingvalues.

F.

Yes, because it is between the limits separating values.

#7

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

383634281917141312.811.6

The range of the sample data is $_____million. (Type an integer or adecimal.)

The variance of the sample data is _______. (Round to two decimal places asneeded.)

The standard deviation of the sample data is $______million.

(Round to two decimal places asneeded.)

Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities ingeneral?

A.

Yes, because the standard deviation is an unbiased estimator.

B.

No, because the sample is not representative of the whole population.

C.

No, because there is an outlier in the sample data.

D.

Yes, because the sample is random.

#8

Find therange, variance, and standard deviation for the given sampledata, if possible. If the measures of variation can be obtained for thesevalues, do the results makesense?

Biologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotypecodes, where 1=smooth-yellow, 2=smooth-green, 3=wrinkled yellow, and 4=wrinkled-green.

22424233222222221222

Can the range of the sample data be obtained for thesevalues? Choose the correct answer belowand, ifnecessary, fill in the answer box within your choice.

A.

The range of the sample data is _______.

(Type an integer or a decimal. Do notround.)

B.

The range of the sample data cannot be calculated.

Can the standard deviation of the sample data be obtained for thesevalues? Choose the correct answer belowand, ifnecessary, fill in the answer box within your choice.

A.

The standard deviation of the sample data is _______.

(Round to one decimal place asneeded.)

B.

The standard deviation of the sample data cannot be calculated.

Can the variance of the sample data be obtained for thesevalues? Choose the correct answer belowand, ifnecessary, fill in the answer box within your choice.

A.

The variance of the sample data is ______.

(Round to one decimal place asneeded.)

B.

The variance of the sample data cannot be calculated.

Do the results makesense?

A.

The measures of variation make sense because the data isnumeric, so the spread between the values is meaningful.

B.

While the measures of variation can befound, they do not make sense because the data arenominal; theydon't measure or count anything.

C.

It makes sense that the measures of variation cannot be calculated because there is not a large enough sample size to calculate the measures of variation.

D.

The measures of variation do not make sense because the standard deviation cannot be greater than the variance.

#9

A sample of blood pressure measurements is taken for a group ofadults, and those values(mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the twosamples; then compare the variation.

Systolic 117 127 158 98 157 122 116 134 124 118

Diastolic 81 75 74 50 89 88 56 63 70 80

The coefficient of variation for the systolic measurements is ______%.

(Type an integer or decimal rounded to one decimal place asneeded.)

The coefficient of variation for the diastolic measurements is _____%.

(Type an integer or decimal rounded to one decimal place asneeded.)

Compare the variation.

The coefficients of variation for each data set are ________(A- More than 5 percentage points apart, B- within 5 percentage points of each other) Therefore, the systolic measurements vary __________( A- Significantly less than, B-About the same as, C-Significantly more than) the diastolic measurements.

#10.

Use theF-scale measurements of tornadoes listed in the accompanying table. The range of the data is 5.0. Use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the actual standard deviation of thedata, 1.3.

F-scale measurements.

2 0

2 0

3 0

3 2

1 0

4 0

0 2

1 2

3 0

4 0

1 2

2 0

2 0

1 2

1 0

3 0

2 0

0 0

3 0

5 2

2 2

0 4

0 0

1 3

0 0

0 0

2 0

0 0

1 1

2 2

2 0

0 2

0 3

0 2

2 2

0 1

1 0

2 0

1 1

4 0

0 1

2 0

2 2

0 2

0 1

0 0

1 0

0 4

0 0

Using the range rule ofthumb, the standard deviation is approximately _______.

(Type an integer or decimal rounded to one decimal place asneeded.)

Compare the result to the actual standard deviation.

The estimated standard deviation is ______(A-less than 0.3 from, B- more than 0.5 from, C- between 0.3 and 0.5 from)

the actual standard deviation.Thus, the estimated standard deviation ________(A- is, B- is not) substantially different from the actual standard deviation.

#11

A certain group of test subjects had pulse rates with a mean of 84.4 beats per minute and a standard deviation of 11.8 beats per minute. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 68.0 beats per minute significantly low or significantlyhigh?

Significantly low values are _____ beats per minute or lower.

(Type an integer or a decimal. Do notround.)

Significantly high values are _______beats per minute or higher.

(Type an integer or a decimal. Do notround.)

Is a pulse rate of 68.0 beats per minute significantly low or significantlyhigh?

A.

Significantlyhigh, because it is morethan two standard deviations above the mean.

B.

Significantlylow, because it is morethan two standard deviations below the mean.

C.

Neither, because it is within two standard deviations of the mean.

D.

It is impossible to determine with the information given.