This food is designed to acquaint the student v the ethics of descriptive and inferential statistics. Topics will certainly include: species of data, frequency distributions and histograms, actions of main tendency, steps of variation, probability, probability distributions consisting of binomial, normal probability and also student's t distributions, traditional scores, to trust intervals, theory testing, correlation, and also linear regression analysis. This course is open up to any type of student interested in basic statistics and also it will include applications pertaining to students majoring in strong training, pre-nursing and business.

You are watching: The range rule of thumb roughly estimates the standard deviation of a data set as _______.


Listed below are the height 10 annual salaries​ (in millions of​ dollars) that TV personalities.

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the provided sample data in millions of dollars.

(e) provided that these room the height 10​ salaries, perform we recognize anything about the incomes of TV personalities in​ general?

(f) space such top 10 lists beneficial for getting insight into the larger​ population?


a. The median is 20.60.

b. The average is 14.25.

c. over there is no mode.

d. The midrange is 23.85.

e. due to the fact that the sample values room the 10​ highest, lock give virtually no information about the wages of TV personalities in general.

f. No, since such optimal 10 perform represent an extreme subset the the populace rather than the bigger population


Listed listed below are the yearly tuition quantities of the 10 most expensive colleges in a nation for a recent year.

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

What walk this​ "Top 10" list tell us around the populace of every one of that​ country"s college​ tuitions?


The median of the data collection is ​$52329.7.

The midrange of the data set is ​$52490.0.

The median of the data set is ​$52274.0.

The​ mode(s) that the data set is​ (are) ​$52297.

Nothing coherent can be concluded from this information except that these are the largest tuitions of colleges in the country for a recent year.


Listed below are the playing times​ (in seconds) of songs the were famous at the moment of this writing.

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange because that the provided sample data.

(e) Is over there one time that is an extremely different indigenous the​ others?


a. The mean is 259.8 seconds.

b. The mean is 243.0 seconds.

c. The setting is 243 & 216 seconds.

d. The midrange is 333.5 seconds.

e. Yes; the moment of 451 secs is really different from the others.


An insurance institute conducted tests v crashes of brand-new cars travel at 6​ mi/h. The total cost the the loss was uncovered for a straightforward random sample the the experiment cars and detailed below.

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange because that the given sample data.

(e) carry out the various measures of facility differ very​ much?


a. The average is ​$6362.6.

b. The average is ​$6332.0.

c. there is no mode.

d. The midrange is ​$6608.5.

e. The different measures of center do no differ through very huge amounts.


Listed listed below are the command concentrations​ (in mg/g) measure in different samples that a medicine.

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

What perform the outcomes suggest around the safety of this​ medicine?

What carry out the decimal worths of the noted amounts suggest around the precision the the​ measurements?


The mean of the data set is 10.60 ​mg/g.

The midrange the the data set is 11.50​mg/g.

The average of the data collection is 10.75 ​mg/g.

The​ mode(s) of the data collection is​ (are) 4.5.

There is not enough information for any kind of meaningful conclusion.

They are rounded come one half unit measurements.


Listed below are the measured radiation emissions​ (in W/kg) equivalent to cell​ phones: A,​ B, C,​ D, E,​ F, G,​ H, I,​ J, and K respectively. The media often present reports around the dangers of cell phone radiation together a reason of cancer. Mobile radiation should be 1.6​ W/kg or less.

Find the a.​ mean, b.​ median, c.​ midrange, and also d. Setting for the data.

e. If you space planning to acquisition a cell​ phone, are any kind of of the actions of center the most important​ statistic? Is there an additional statistic the is most​ relevant? If​ so, which​ one?


a. The median is 0.930.

b. The mean is 0.870.

c. The midrange is 0.990.

d. over there is no mode.

e. The maximum data worth is the many relevant​ statistic, since it is closest come the limit of​ 1.6W/kg and that cabinet phone have to be avoided.


Listed listed below are the errors in between the guess temperatures and also actual temperature of a certain city.

Find the mean and median for each the the 2 samples.

Do the way and medians suggest that the temperature predicted one day in advancement are an ext accurate than those predicted 5 days in​ advance, together we might​ expect?


The average difference between actual high and the predicted high one day earlier is 0.5°.

The typical difference in between actual high and the predicted high one day earlier is 1.0°.

The mean difference between actual high and the suspect high 5 days previously is -0.3°.

The median difference in between actual high and the suspect high 5 days previously is 2.0°.

No, the means and medians execute not indicate any considerable difference in accuracy.


Statistics are occasionally used to to compare or identify authors of different works. The lengths of the an initial 10 words in a book by terry are noted with the an initial 10 indigenous in a publication by David.

Find the mean and median because that each that the two​ samples.

Compare the 2 sets of results. Walk there show up to be a​ difference?


The mean variety of letters every word in​ Terry"s publication is 3.5.

The median variety of letters every word in​ Terry"s publication is 3.0.

The mean number of letters every word in​ David"s publication is 3.1.

The median number of letters per word in​ David"s publication is 3.0.

Yes. Based upon the​ results, words in​ Terry"s book are much longer than the words in​ David"s book.


Waiting times​ (in minutes) of customers in a financial institution where every customers enter a solitary waiting line and a financial institution where customers wait in individual lines at three different teller home windows are listed below.

Find the mean and also median for each that the two​ samples.

Determine whether over there is a difference in between the two data sets the is not obvious from a comparison of the measures of center. If​ so, what is​ it?


The average waiting time for customers in a single line is 7.11 minutes.

The mean waiting time for customers in a single line is 7.10 minutes.

The average waiting time because that customers in separation, personal, instance lines is 7.11 minutes.

The typical waiting time for customers in individual lines is 7.10 minutes.

The times because that customers in separation, personal, instance lines space much an ext varied than the times because that customers in a single line.

Notice the the mean and also median waiting times for customers in solitary and separation, personal, instance lines are the same. To determine if over there is a difference in between the 2 data sets that is not evident from the compare of the means and​ medians, compare how the data values vary amongst themselves in each set.


Use the magnitudes​ (Richter scale) that the earthquakes detailed in the data collection below.

Find the mean and median of this data set.

Is the magnitude of one earthquake measure 7.0 ~ above the Richter scale an outlier​ (data value that is really far far from the​ others) when thought about in the paper definition of the sample data offered in this data​ set? Explain.


The typical of the data collection is 1.452.

The average of the data set is 1.470.

Yes, due to the fact that this worth is an extremely far far from all of the various other data values.


Find the typical of the data summarized in the given frequency distribution.

Compare the computed median to the actual average of 52.3°.


The mean of the frequency distribution is 52.5°.

<(1 x 42) + (6 x 47) + (13 x 52) + (7 x 57) + (2 x 62)> ÷ 29 = 52.52

The computed mean is close to the yes, really mean due to the fact that the difference in between the way is less than​ 5%.


Find the median of the data summarized in the provided frequency distribution.

Compare the computed mean to the actual mean of 46.6 miles per hour.


The average of the frequency distribution is 46.5 miles per hour.

<(28 x 43.5) + (16 x 47.5) + (6 x 51.5) + (3 x 55.5) + (1 x 59.5)> ÷ 54 = 46.54

The computed typical is close to the actual mean since the difference between the method is much less than​ 5%.


The geometric median is frequently used in business and economics for finding typical rates of​ change, mean rates of​ growth, or mean ratios. Provided n values​ (all of which are​ positive), the geometric median is the nth root of their product.

The average development factor for money compounded at yearly interest rates of 14​%, 6​%, and 3​% can be uncovered by computing the geometric average of 1.14, 1.06​, and 1.03. Find that average expansion factor.

The single percentage growth rate is uncovered by individually 1 from the expansion factor and also then multiply by​ 100%. What solitary percentage expansion rate would be the same as having actually three successive expansion rates the 14​%, 6​%, and also 3​%?

Is that result the exact same as the typical of 14​%, 6​%, and 3​%?


The average expansion factor is 1.0757.

(1.14 x 1.06 x 1.03)^(1/3) = 1.075678893

The solitary percentage growth rate that would be the same as having three successive development rates of 14​%, 6​%, and 3​% is 7.57%​.

(1.0757 – 1) x 100 = 7.57

The typical of 14​%, 6​%, and 3​% is 7.67%.

The solitary percentage expansion rate is not the exact same as the median of 14​%, 6​%, and 3%.


descriptive

Descriptive statistics space methods and tools the summarize or describe relevant attributes of data.


census

A census is the arsenal of data indigenous every member that the population. That is no a measure up of center.


Listed below are the optimal 10 yearly salaries​ (in millions of​ dollars) that TV personalities.

Find the​ range, variance, and standard deviation because that the sample data.

Given that these space the peak 10​ salaries, is the standard deviation that the sample a great estimate of the sports of wages of TV personalities in​ general?


The selection of the sample data is ​$33.5 million.

The variance the the sample data is 191.10.

The conventional deviation the the sample data is ​$13.82 million.

No, due to the fact that the sample is not representative that the whole population.


Six different​ second-year medical students in ~ Bellevue Hospital measured the blood push of the exact same person. The systolic readings​ (in mmHg) are listed below.

Find the​ range, variance, and also standard deviation for the offered sample data.

If the​ subject"s blood push remains constant and the clinical students correctly apply the very same measurement​ technique, what should be the value of the standard​ deviation?


Range = 18 mmHg

Sample variance = 43.1 mmHg²

Sample typical deviation = 6.6 mmHg

Ideally, the traditional deviation would be zero since all the measurements should be the same.


Listed listed below are the amounts of mercury​ (in parts per​ million, or​ ppm) discovered in tuna episode sampled at different stores.

Find the​ range, variance, and also standard deviation for the collection of data.

What would certainly be the worths of the measures of sport if the tuna sushi consisted of no​ mercury?


The range of the sample data is 0.97 ppm.

Sample variance = 0.140 ppm²

Sample conventional deviation = 0.374 ppm

The procedures of variation would all it is in 0.


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Listed below are the arrival hold-up times​ (in minutes) that randomly selected airplane flights native one airport to another. An unfavorable values correspond to flights the arrived early before the reserved arrival​ time, and positive values stand for lengths that delays.

Find the​ range, variance, and standard deviation for the set of data.

Some of the sample values are​ negative, yet can the standard deviation ever be​ negative?


The selection of the sample data is 41 minutes.

The variance that the sample data is 200.5 minutes².

The traditional deviation that the sample data is 14.2 minutes.

​No, since the squared value in the conventional deviation formula can not be negative.


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Listed below are amounts​ (in millions of​ dollars) gathered from parking meter by a security service firm and various other companies during similar time periods.

Find the coefficient of variation for each that the two​ samples, then compare the variation.

Do the restricted data noted here present evidence of steal by the defense service​ company"s employees? consider a difference of better than​ 1% to be significant.


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The coefficient of variation for the amount gathered by the defense service company is 9.98​%.

(0.1567021236 ÷ 1.57) x 100 = 9.981026981

The coefficient of variation for the amount gathered by the other companies is 7.65​%.

(0.1316561177 ÷ 1.72) x 100 = 7.654425448

Yes. There is a significant difference in the variation.


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Listed below are contributions​ (in dollars) make to 2 presidential candidates in a recent election.

Find the coefficient of variance for each data set.

Is there a distinction in variation between the 2 data​ sets? take into consideration a difference of greater than​ 1% to be significant.


The coefficient that variation because that the contribute to Candidate A is 46.36​%.

The coefficient that variation because that the contribute to Candidate B is 70.39​%.

The contributions to Candidate A have substantially less variation than the contribute to Candidate B.


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Refer to the data collection of times required to taxi the end for​ takeoff, noted below in minutes.

Use modern technology to find the​ range, variance, and standard deviation.


The range of the data set is 40 minutes.

The​ variance, s²​, the the data collection is 151.4 minutes².

The standard​ deviation, s, the the data collection is 12.3 minutes.


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Below are the variety and standard deviation for a set of data.

Use the variety rule of thumb and compare it come the typical deviation noted below.

Does the selection rule that thumb develop an acceptable​ approximation? mean a researcher deems the approximation as acceptable if it has an error less than​ 15%.


The approximated standard deviation is 0.695.

2.78 ÷ 4 = 0.695

No, because the error the the range rule of​ thumb"s approximation is better than​ 15%.


A particular group of test subjects had pulse rates with a average of 77.6 beats every minute and a typical deviation of 10.2 beats per minute.

Would it it is in "unusual" for one of the test topics to have a pulse price of 68.0 beats per​ minute?


Minimum​ "usual" worth = 57.2 beats per minute

minimum​ "usual" value = ​(mean) 2 x (standard ​deviation)

77.6 – 2(10.2) = 57.2

Maximum​ "usual" value = 98.0 beats per minute

minimum​ "usual" worth = ​(mean) + 2 x (standard ​deviation)

77.6 – 2(10.2) = 98.0

No, since it is in between the minimum and maxmum "usual" values.


Cans of constant soda have actually volumes through a average of 13.51 oz and a standard deviation that 0.12 oz.

Is that "unusual" for a deserve to to contain 13.59 oz that soda?


Minimum​ "usual" value = 13.27 oz

Maximum​ "usual" worth = 13.75 oz

No, since it is between the minimum and maxmum "usual" values.


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Find the standard​ deviation, s, that sample data summary in the frequency distribution table given below by utilizing the formula​ below, where x to represent the class​ midpoint, f represents the class​ frequency, and also n to represent the total number of sample values.​

Compare the computed typical deviation come the typical deviation obtained from the initial list that data​ values, 9.0. Take into consideration a difference of​ 20% in between two values of a traditional deviation to it is in significant.


Standard deviation = 7.7

---------------------------------------------------------------------------------

(Use calculator)

L1 L2

midpt freq

1–Var Stats L1,L2

Sx = 7.679830596

---------------------------------------------------------------------------------

The computed value is not substantially different from the provided value.


Heights of men on a baseball team have a​ bell-shaped distribution with a average of 178 cm and a typical deviation the 8 cm.

Using the empirical​ rule, what is the approximate percentage of the men in between the following​ values?

a. 154 cm and also 202 cm

b. 170 cm and also 186 cm


a. 99.73​% the the guys are between 154 cm and 202 cm.

(154 178) ÷ 8 = -3

(202 – 178) ÷ 8 = 3

3 SD... 99.73%

b. 68​% the the guys are in between 170 cm and also 186 cm.

(170 178) ÷ 8 = -1

(186 – 178) ÷ 8 = 1

1 SD... 68%

one standard deviation indigenous the mean accounts for about 68% the the set two standard deviations native the median account for around 95% three standard deviations indigenous the median account for around 99.7%.

Which that the complying with is not a home of the standard​ deviation?

A. The value of the typical deviation is never negative.

B. As soon as comparing sports in samples with very different​ means, that is great practice to compare the two sample conventional deviations.

C. The typical deviation is a measure up of sport of every data values from the mean.

D. The devices of the standard deviation are the exact same as the devices of the initial data.


B. Once comparing variation in samples with an extremely different​ means, the is great practice to to compare the two sample standard deviations.

It"s a good practice to compare 2 sample standard deviations only as soon as the sample method are roughly the same. When comparing variation in samples with an extremely different means, that is better to usage the coefficient that variation, i m sorry is characterized later in this section.


variance

The term variance has a specific statistical meaning and is same to the square that the traditional deviation.


If your score top top your following statistics check is convert to a z​ score, i m sorry of this z scores would you​ prefer: –​2.00, –1.00, ​0, 1.00,​ 2.00? Why?


The z score that 2.00 is many preferable due to the fact that it is 2.00 typical deviations above the mean and also would correspond to the highest of the five different feasible test scores.

A z score​ (or standardized​ value) is the variety of standard deviations that a provided value x is above or listed below the mean. A an unfavorable z score coincides to an x value less than the mean. A optimistic z score corresponds to an x value better than the mean. The more negative the z​ score, the further the x value is below the mean. The an ext positive the z​ score, the additional the x worth is over the mean.


With a elevation of 68 ​in, George was the shortest president of a certain club in the past century. The society presidents of the previous century have actually a mean elevation of 73.7 in and a conventional deviation that 2.7 in.

a. What is the confident difference between George​"s height and also the​ mean?

b. How numerous standard deviations is that​ ?

c. Convert George​"s elevation to a z score.

d. If us consider​ "usual" heights to it is in those that convert to z scores between –2 and​ 2, is George​"s height usual or​ unusual?


a. The hopeful difference between George​"s height and the mean is 5.7 in.

( height mean )

b. The distinction is 2.11 standard deviations.

(positive distinction ÷ standard deviation)

c. The z score is –2.11.

(difference ÷ standard deviation)

d. Unusual


A details group the men have actually heights v a typical of 173 cm and also a typical deviation that 7 cm. Carl had actually a height of 180 cm.

a. What is the optimistic difference in between Carl​"s height and also the​ mean?

b. How numerous standard deviations is that​ ?

c. Convert Carl​"s height to a z score.

d. If we consider​ "usual" heights to be those that convert to z scores in between –2 and​ 2, is Carl​"s height usual or​ unusual?


a. The confident difference in between Carl​"s height and the average is 7 cm.

( height mean )

b. The distinction is 1 conventional deviations.

(positive difference ÷ standard deviation)

c. The z score is 1.

(difference ÷ standard deviation)

d. Usual


IQ scores space measured with a check designed so the the typical is 100 and also the typical deviation is 18. Think about the team of IQ scores that space unusual.

What room the z scores that separate the inexplicable IQ scores indigenous those that are​ usual?

What room the IQ scores that separate the unexplained IQ scores indigenous those the are​ usual? (Consider a worth to be inexplicable if its z score is much less than –2 or higher than​ 2.)


The lower z score boundary is –2.

The greater z score boundary is 2.

The reduced bound IQ score is 64.

(lower z score x conventional deviation) + mean

The higher bound IQ score is 136.

(higher z score x typical deviation) + mean


In a current year the magnitudes​ (Richter scale) of​ 10,594 earthquakes to be recorded. The mean is 1.218 and also the conventional deviation is 0.584. Take into consideration the magnitudes that are unusual.

What are the magnitudes that different the inexplicable magnitudes native those the are​ usual? ​(Consider a value to be unexplained if that z score is less than –2 or higher than​ 2.)


The reduced bound earthquake size is 0.05.

(lower z score x traditional deviation) + mean

The greater bound earthquake magnitude is 2.386.

(higher z score x traditional deviation) + mean


One that the tallest life men has a height of 261 cm. Among the tallest living women is 243 cm tall. Heights of men have a average of 170 cm and a conventional deviation the 8 cm. Heights that women have actually a average of 159 cm and a traditional deviation the 3 cm.

Relative to the population of the same​ gender, who is​ taller? Explain.


The woman is relatively taller due to the fact that the z score for her height is greater than the z score because that the man​"s height.

Man z score = (261 – 170) ÷ 8 = 11.375

Woman z score = (243 – 159) ÷ 3 = 28


Which is relatively​ better: a score that 52 on a psychology test or a score that 46 on an economics​ test? Scores ~ above the psychology test have a median of 94 and also a typical deviation that 15. Scores on the business economics test have actually a mean of 55 and a typical deviation that 5.


The business economics test score is relatively much better because that z score is higher than the z score because that the psychology test score.

Psych = (52 – 94) ÷ 15 = –2.8

Econ = (46 – 55) ÷ 5 = –1.8


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Below are 36 sorted periods of an exhilaration award winner.

Find the percentile corresponding to age 32 making use of the method presented in the textbook.


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percentile of worth 32 = 25

percentile of worth x = number of values much less than x ÷ total variety of values x 100

9 ÷ 36 x 100 = 25.0


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Below are 36 sorted periods of an exhilaration award winner.

Find the percentile equivalent to age 60 using the technique presented in the textbook.


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percentile of value 60 = 61

percentile of value x = variety of values less than x ÷ total number of values x 100

22 ÷ 36 x 100 = 61.1


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Below room 36 sorted periods of an exhilaration award winner.

Find P80 making use of the an approach presented in the textbook.


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P80 = 67

L = (k ÷ 100) x n

= (80 ÷ 100) x 36 = 28.8 = 29

The worth of P80 is the 29th value, counting native the lowest. The 29th worth is 67.


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Find the 3rd quartile Q3 that the list of 24 sorted values displayed below.


The 3rd quartile Q3 is 60.

Quartiles are actions of​ location, denoted Q1​, Q2​, and also Q3, which divide a collection of data into four groups through about​ 25% that the worths in every group. Note that quartiles and percentiles are connected ​(Q1 = P25​, Q2 = P50​, and also Q3 = P75 ).

L = k ÷ 100 x n

75 ÷ 100 x 24 = 18

Since together = 18 is a whole​ number, to uncover P75​, add the 18th value and also the following value in the sorted collection of data and also divide the full by 2.

The 18th value is 59. The 19th value is 61.

59 + 61 = 120

120 ÷ 2 = 60

Since P75 = 60​, the third quartile Q3 is 60.


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Below space 36 sorted eras of an exhilaration award winner.

Find P75 utilizing the technique presented in the textbook.


P75 = 68.5

L = k ÷ 100 x n

75 ÷ 100 x 36 = 27

What is the Lth = 27th worth in the sorted​ list? 67

What is the following value in the sorted​ list? 70

P75 = (67 + 70) ÷ 2 = 68.5


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Below space 36 sorted eras of an acting award winner.

Find P50 using the technique presented in the textbook.


P50 = 47.5

L = k ÷ 100 x n

50 ÷ 100 x 36 = 18

What is the Lth = 18th worth in the sorted​ list? 47

What is the following value in the sorted​ list? 48

P50 = (47 + 48) ÷ 2 = 47.5


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The adhering to are the duration times​ (minutes) the all objectives flown by a an are shuttle.

Use the given data to construct a boxplot and identify the​ 5-number summary.


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The​ 5-number review is 6, 8603, 10014, 11407, 11809.

For a set of​ data, the​ 5-number an introduction consists the the 5 values detailed below.

1. Minimum

2. First​ quartile, Q1

3. Second​ quartile, Q2​ (same as the​ median)

4. Third​ quartile, Q3

5. Maximum

(Use Calculator)


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The complying with are the interval times​ (minutes) between eruptions of a geyser.

Detemine the 5 number review and build a crate plot native the data below.


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The​ 5-number an overview is 81, 87, 92.5, 98, 109.


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The complying with are amounts of time​ (minutes) invested on hygiene and grooming in the morning by survey respondents.

Determine the​ 5-number an introduction and construct a boxplot because that the data offered below.


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The​ 5-number an introduction is 4​, 10​, 19​, 38​, 62.


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The complying with are speeds​ (mi/h) of dare measured with a radar gun.

Determine the​ 5-number summary and boxplot because that the data provided below.


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The​ 5-number an overview is 70​, 71​, 74​, 78​, 79


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Use the same scales to construct boxplots because that the pulse prices of males and females from the accompanying data sets.

Use the boxplots to to compare the two data sets.


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Men"s: 46, 60, 67, 75,92

Women"s: 57, 72, 77, 82.5, 105

In​ general, it appears that males have lower pulse prices than females. The variation among the male pulse rates is comparable to the variation among the woman pulse rates.


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Use the exact same scale to construct boxplots for the ages of the finest actors and also best actresses indigenous the accompanying data sets.

Use the boxplots to compare the two data sets.


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Actor"s: 30, 37, 42.5, 50, 76

Actresses: 22, 29, 33.5, 38.5, 80

Although actresses include the oldest​ age, the boxplot representing actresses reflects that they have eras that are typically lower 보다 those the actors.


When a data value is converted to a standardized scale representing the variety of standard deviations the data worth lies from the​ mean, we speak to the new value a​ _______.


z-score

The term​ z-score to represent a standardized value and also is the number of standard deviations the a given​ x-value is above or listed below the mean.


unusual

A data value is thought about unusual when it lies far from the mean. We specify data values that are more than 2 conventional deviations far from the average as unusual.


the matching z-score is negative

A negative​ z-score indicates a data worth is much less than the mean.


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

See more: True Or F A Bill Of Materials For A Menu Item In A Restaurant Is Also Called A L


outlier

For the purposes of building modified​ boxplots, outliers are any type of data values above Q3 + (1.5)(IQR) or below Q1 – ​(1.5)(IQR).