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.

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 **σ**² .

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.

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.

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.

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%.*

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.

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

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.

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.

*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.**