This food is designed come acquaint the student with the ethics of descriptive and inferential statistics. Topics will include: varieties of data, frequency distributions and also histograms, actions of main tendency, measures of variation, probability, probability distributions including binomial, regular probability and student's t distributions, typical scores, confidence intervals, theory testing, correlation, and also linear regression analysis. This food is open up to any kind of student interested in basic statistics and it will encompass applications pertaining come students majoring in athletic training, pre-nursing and business.

You are watching: The measure of center that is the value that occurs with the greatest frequency is the _______.


In an​ editorial, the Poughkeepsie Journal printed this​ statement: "The median price – the price exactly in in between the highest and also lowest – ..." does this explain correctly explain the​ median? Why or why​ not?


Which the the adhering to is always​ true?

A. Data it was crooked to the right have actually a much longer left tail than right tail.

B. In a symmetric and​ bell-shaped distribution, the​ mean, median, and also mode room the same.

C. Because that skewed​ data, the setting is farther the end in the longer tail 보다 the median.

D. The mean and median need to be provided to recognize the shape of the distribution.


Pennies made before 1983 are​ 97% copper and​ 3% zinc, vice versa, pennies make after 1983 are​ 3% copper and​ 97% zinc. Listed below room the weights​ (in grams) the pennies from each of the 2 time periods.

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

Does there show up to it is in a significant difference in the​ means?


The typical weight that the pennies made before 1983 is 3.1133 grams.

The typical weight that the pennies made prior to 1983 is 3.10645 grams.​

The median weight that the pennies made after 1983 is 2.4926 grams.​

The mean weight the the pennies do after 1983 is 2.49315 grams.​

​Yes, due to the fact that the difference in the means is more than​ 5%.


Listed listed below are head injury measurements from small cars that were experiment in crashes. The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" worths correspond come safer​ cars). The detailed values exchange mail to cars​ A, B,​ C, D,​ E, F, and​ G, respectively.

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

e. I beg your pardon car shows up to be the​ safest?

f. Based upon these limited​ results, do small cars show up to have around the very same risk the head injury in a​ crash?


a. The typical is 417.7.​

b. The typical is 392.​

c. The midrange is 425.

d. over there is no mode.

e. automobile E

f. No, because the data worths differ substantially.


Because the average is an extremely sensitive come extreme​ values, that is no a resistant measure of center. The trimmed median is an ext resistant. To discover the​ 10% trimmed typical for a data​ set, an initial arrange the data in​ order, climate delete the bottom​ 10% that the values and the top​ 10% that the​ values, then calculation the median of the remaining values.

For the following​ credit-rating scores, discover ​(a) the​ mean, (b) the​ 10% trimmed​ mean, and​ (c) the​ 20% trimmed mean.

How execute the results​ compare?


a. The typical is 720.5.

b. The​ 10% trimmed typical is 729.3.​

c. The​ 20% trimmed mean is 734.3.

The circulation of the data appears to be skewed to the left since the results appear to present a tendency of raising values as the percentage of trim increases.


Listed below are the durations​ (in hours) that a an easy random sample of every flights of a room shuttle.

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the offered sample data.

(e) Is over there a duration time that is very​ unusual? How can that expression time be​ explained?


a. The average is 218.7 hours.​

b. The median is 239.0 hours.

c. The setting is 239 hours.

d. The midrange is 192.0 hours.

e. Yes, the time of 0 hours is very unusual. It might represent a flight that to be aborted.


An experiment was carried out to recognize whether a deficiency the carbon dioxide in the floor affects the phenotype that peas. Listed below room the phenotype codes where 1 equals smooth dash yellow​, 2 equals smooth dash green​, 3 equals wrinkled dash yellow​, and also 4 equals wrinkled dash green.

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the offered sample data.

(e) execute the outcomes make​ sense?


a. The typical phenotype password is 2.9.​

b. The median phenotype password is 3.0.

c. The mode phenotype password is 3.

d. The midrange that the phenotype password is 2.5.

e. just the mode makes sense because the data is nominal.


Refer come the data set of​ times, in​ minutes, forced for an plane to taxi the end for​ takeoff, detailed below.

Find the mean and also median.

How is it advantageous to find the​ mean?


The median of the data collection is 28.5 minutes.​

The mean of the data collection is 27.0 minutes.

The mean taxi out time is crucial for calculating and scheduling the come time.


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Below space the variety and typical deviation because that a set of data.

Use the range rule of thumb and also compare it come the standard deviation provided below.

Does the range rule the thumb create an acceptable​ approximation? mean a researcher deems the approximation together acceptable if it has actually an error less than​ 15%.


The estimated standard deviation is 0.730

No, due to the fact that the error the the selection rule of​ thumb"s approximation is greater than​ 15%.


Cans of constant soda have actually volumes v a mean of 12.01 oz and a conventional deviation the 0.11 oz.

Is it unexplained for a deserve to to save 12.11 oz of​ soda?


Minimum​ "usual" worth = 11.79 oz

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

Maximum​ "usual" worth = 12.23 oz

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

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


Cans of continual soda have volumes with a typical of 12.24 oz and also a traditional deviation of 0.11 oz.

Is it unusual for a have the right to to save 12.58 oz of​ soda?


Minimum​ "usual" value = 12.02 oz

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

Maximum​ "usual" worth = 12.46 oz

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

Yes, since it is larger than the maximum "usual" value.


Identify the symbols supplied for every of the​ following: (a) sample standard​ deviation; (b) populace standard​ deviation; (c) sample​ variance; (d) populace variance.


a. The symbol because that sample traditional deviation is s.

b. The prize for population standard deviation is σ .

c. The symbol for sample variance is s²

d. The prize for populace variance is σ² .


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The tendency of thinner beauty pageant winners has generated charges that the dispute encourages unhealthy diet habits amongst young women. Noted below room body mass indexes​ (BMI) for beauty pageant winners indigenous two different time periods.

Find the coefficient the variation for each of the 2 sets of​ data.

Is over there a distinction in variation between the two data​ sets?


The coefficient that variation because that the​ BMI"s of beauty beauty pageant winners from the 1920s and also 1930s is 7.50​%.

CV = was standing dev ÷ median x 100%

The coefficient that variation because that the​ BMI"s of recent beauty pageant winners is 6.37​%.

There is no far-ranging difference in the variations.


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Waiting times​ (in minutes) of client at a bank where all customers get in a solitary waiting line and also a bank where customers wait in individual lines at three different teller windows are provided below.

Find the coefficient that variation because that each the the two sets of​ data.

Is there a difference in variation in between the two data​ sets?


The coefficient the variation for the waiting times at financial institution A is 6.41​%.

CV = was standing dev ÷ mean x 100%

The coefficient that variation because that the waiting times at the bank B is 24.61​%.

The wait times at bank A have considerably less variation than the wait times at financial institution B.


Which that the complying with is no a home of the standard​ deviation?

A. Once comparing sports in samples with an extremely different​ means, it is good practice to to compare the 2 sample traditional deviations.

B. The worth of the typical deviation is never negative.

C. The standard deviation is a measure of variation of all data values from the mean.

D. The devices of the traditional deviation are the same as the systems of the original data.


A. When comparing sport in samples with an extremely different​ means, it is an excellent practice to compare the two sample traditional deviations.


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Listed below are the pistol amounts​ (in millions of​ dollars) earn in crate office receipts for a current movie. The amounts are detailed in order because that the an initial 14 days of the movies release.

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

If you invested in this​ movie, what characteristics of the data collection would you treatment about​ most, and is the a measure of center or​ variation?


The variety of the sample data is 55 million dollars.

The variance the the sample data is 366.8 million dollars².

The standard deviation that the sample data is 19.2 million dollars.

The gun from opening day and also the price of decline. The procedures of center and variation are less important.


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

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

What would certainly be the worths of the actions of sport if the tuna sushi included no​ mercury?


The range of the sample data is 0.48 ppm.

Sample variance = 0.029 ppm²

Sample traditional deviation = 0.171 ppm

The actions of variation would all it is in 0.


Heights of males on a baseball team have actually a​ bell-shaped circulation with a mean of 182 cm and a conventional deviation of 7 cm.

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

a. 168 cm and 196 cm

b. 161 cm and also 203 cm


a. 95​% the the guys are in between 168 cm and 196 cm.

b. 99.7​% that the males are in between 161 cm and also 203 cm.

one conventional deviation native the median accounts for around 68% the the set two conventional deviations native the typical account for about 95% three traditional deviations from the typical account for around 99.7%.
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The complying with are quantities of time​ (minutes) spent on hygiene and grooming in the morning by inspection respondents.

Determine the​ 5-number summary and build a boxplot because that the data offered below.


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The​ 5-number an introduction is 6​, 11​, 18.5​, 37​, 62.


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Below room 36 sorted periods of an exhilaration award winner.

Find P70 utilizing the an approach presented in the textbook.


P70 = 66

L = k ÷ 100 x n

70 ÷ 100 x 36 = 25.2 (round up)

What is the Lth = 26th value in the sorted​ list? 66

What is the next value in the sorted​ list? 66

P75 = (66 + 66) ÷ 2 = 66


IQ scores space measured v a test designed so the the median is 103 and the conventional deviation is 13. Think about the team of IQ scores that room unusual.

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

What room the IQ scores that different the unusual IQ scores native those the are​ usual?(Consider a value to be unexplained if its z score is much less than –2 or better than​ 2.)


The lower z score border is –2.

The greater z score border is 2.

The lower bound IQ score is 64.

(lower z score x traditional deviation) + mean

The greater bound IQ score is 136.

(higher z score x standard deviation) + mean


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


The z score the 2.00 is many preferable because it is 2.00 conventional deviations above the mean and would correspond to the highest of the five different possible test scores.


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Use the very same scale to construct boxplots because that the periods of the ideal actors and best actresses native the accompanying data sets.

Use the boxplots to compare the two data sets.


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Actors: 27, 37, 43, 50, 76

Actresses: 21, 28, 33, 39, 82

Although actresses encompass the oldest​ age, the boxplot representing actresses reflects that castle have eras that are generally lower than those of actors.


Which is relatively​ better: a score that 76 on a psychology check or a score of 45 on one economics​ test? Scores ~ above the psychology test have actually a mean of 89 and a typical deviation of 5. Scores on the economics test have actually a typical of 55 and also a conventional deviation the 7.

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The economics test score is relatively far better because its z score is better than the z score for the psychology test score.