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

Which of the complying with is always true?

A. File skewed to the appropriate have actually a much longer left tail than right tail.

B. In a symmetric and bell-shaped distribution, the intend, median, and also mode are the very same.

C. For skewed information, the mode is farther out in the much longer tail than the median.

D. The suppose and also median should be provided to identify the form of the circulation.

Pennies made prior to 1983 are 97% copper and 3% zinc, whereas pennies made after 1983 are 3% copper and 97% zinc. Listed listed below are the weights (in grams) of pennies from each of the 2 time durations.

Find the mean and median for each of the two samples.

Does there appear to be a significant difference in the means?

The suppose weight of the pennies made prior to 1983 is 3.1133 grams.

The median weight of the pennies made prior to 1983 is 3.10645 grams.

The intend weight of the pennies made after 1983 is 2.4926 grams.

The median weight of the pennies made after 1983 is 2.49315 grams.

Yes, bereason the distinction in the indicates is more than 5%.

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

Find the a. suppose, b. median, c. midrange, and also d. mode for the information.

e. Which vehicle shows up to be the safest?

f. Based on these limited results, carry out small cars show up to have around the exact same hazard of head injury in a crash?

**a.** The suppose is 417.7.

**b.** The median is 392.

**c.** The midvariety is 425.

**d.** Tbelow is no mode.

**e.** auto E

**f.** No, because the data worths differ considerably.

Since the expect is exceptionally sensitive to extreme worths, it is not a resistant meacertain of center. The trimmed mean is even more resistant. To uncover the 10% trimmed suppose for a data collection, initially arselection the data in order, then delete the bottom 10% of the values and the top 10% of the values, then calculate the intend of the staying values.

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

How do the results compare?

**a.** The intend is 720.5.

**b.** The 10% trimmed suppose is 729.3.

**c.** The 20% trimmed suppose is 734.3.

The circulation of the information appears to be skewed to the left bereason the results appear to present a trfinish of increasing values as the portion of trim boosts.

Listed listed below are the durations (in hours) of an easy random sample of all flights of a space shuttle.

Find the (a) suppose, (b) median, (c) mode, and (d) midrange for the provided sample information.

(e) Is tbelow a duration time that is very unusual? How can that duration time be explained?

**a.** The expect is 218.7 hrs.

**b.** The median is 239.0 hrs.

**c.** The mode is 239 hrs.

**d.** The midselection is 192.0 hours.

**e.** Yes, the time of 0 hours is very unusual. It could represent a flight that was aborted.

An experiment was performed to recognize whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenokind codes wright here 1 equals smooth dash yellow, 2 amounts to smooth dash green, 3 equates to wrinkled dash yellow, and also 4 equates to wrinkled dash green.

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

(e) Do the outcomes make sense?

**a.** The suppose phenokind code is 2.9.

**b.** The median phenotype code is 3.0.

**c.** The mode phenotype code is 3.

**d.** The midselection of the phenokind codes is 2.5.

**e.** Only the mode renders feeling given that the information is nominal.

Refer to the data collection of times, in minutes, required for an plane to taxi out for takeoff, listed listed below.

Find the expect and also median.

How is it advantageous to uncover the mean?

The mean of the data collection is 28.5 minutes.

The median of the data collection is 27.0 minutes.

The suppose taxi out time is necessary for calculating and scheduling the arrival time.

Below are the variety and traditional deviation for a collection of data.

Use the range dominion of thumb and compare it to the conventional deviation provided below.

Does the selection rule of thumb produce an acceptable approximation? Suppose a researcher deems the approximation as acceptable if it has an error less than 15%.

The estimated conventional deviation is 0.730

No, because the error of the selection dominance of thumb"s approximation is better than 15%.

Cans of consistent soda have volumes with a intend of 12.01 oz and also a standard deviation of 0.11 oz.

Is it unexplained for a have the right to to contain 12.11 oz of soda?

Minimum "usual" value = 11.79 oz

*minimum "usual" value = (mean) – 2 x (typical deviation*

Maximum "usual" value = 12.23 oz

*minimum "usual" value = (mean) + 2 x (conventional deviation)*

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

Cans of regular soda have actually volumes via a mean of 12.24 oz and also a traditional deviation of 0.11 oz.

Is it unusual for a can to contain 12.58 oz of soda?

Minimum "usual" worth = 12.02 oz

*minimum "usual" value = (mean) – 2 x (conventional deviation*

Maximum "usual" value = 12.46 oz

*minimum "usual" value = (mean) + 2 x (traditional deviation)*

Yes, because it is larger than the maximum "usual" worth.

Identify the icons supplied for each of the following: (a) sample standard deviation; (b) populace standard deviation; (c) sample variance; (d) population variance.

**a.** The symbol for sample standard deviation is s.

**b.** The symbol for population traditional deviation is **σ** .

**c.** The symbol for sample variance is s²

**d.** The symbol for populace variance is **σ**² .

The trend of thinner beauty pageant winners has actually produced charges that the challenge urges unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for beauty pageant winners from 2 different time periods.

Find the coeffective of variation for each of the two sets of data.

Is tright here a distinction in variation in between the two data sets?

The coefficient of variation for the BMI"s of beauty pageant winners from the 1920s and 1930s is 7.50%.

*CV = stand also dev ÷ expect x 100%*

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

Tright here is no considerable distinction in the variations.

Waiting times (in minutes) of customers at a financial institution wright here all customers enter a solitary waiting line and a financial institution wbelow customers wait in individual lines at 3 various teller windows are detailed listed below.

Find the coreliable of variation for each of the 2 sets of data.

Is tbelow a distinction in variation in between the two data sets?

The coefficient of variation for the waiting times at Bank A is 6.41%.

*CV = stand dev ÷ expect x 100%*

The coefficient of variation for the waiting times at the Bank B is 24.61%.

The waiting times at Bank A have substantially less variation than the waiting times at Bank B.

Which of the adhering to is NOT a property of the standard deviation?

A. When comparing variation in samples with extremely different suggests, it is good exercise to compare the two sample standard deviations.

B. The value of the traditional deviation is never negative.

C. The traditional deviation is a meacertain of variation of all information worths from the mean.

D. The systems of the standard deviation are the very same as the systems of the original data.

A. When comparing variation in samples through extremely different implies, it is great exercise to compare the 2 sample standard deviations.

Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The quantities are detailed in order for the first 14 days of the movies release.

Find the array, variance, and traditional deviation of the data set.

If you invested in this movie, what characteristic of the data set would you treatment about the majority of, and is it a measure of facility or variation?

The range of the sample information is 55 million dollars.

The variance of the sample data is 366.8 million dollars².

The typical deviation of the sample information is 19.2 million dollars.

The gross from opening day and also the price of decrease. The actions of facility and also variation are much less essential.

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

Find the array, variance, and also standard deviation for the set of information.

What would be the values of the steps of variation if the tuna sushi contained no mercury?

The variety of the sample information is 0.48 ppm.

Sample variance = 0.029 ppm²

Sample typical deviation = 0.171 ppm

The actions of variation would certainly all be 0.

Heights of men on a baseball team have actually a bell-shaped circulation via a intend of 182 cm and a typical deviation of 7 cm.

Using the empirical preeminence, what is the approximate percent of the guys between the following values?

**a.** 168 cm and also 196 cm

**b.** 161 cm and also 203 cm

**a.** 95% of the guys are between 168 cm and 196 cm.

**b.** 99.7% of the guys are in between 161 cm and also 203 cm.

*one standard deviation from the intend accounts for around 68% of the set*

*two conventional deviations from the mean account for around 95%*

*three typical deviations from the expect account for about 99.7%.*

The adhering to are quantities of time (minutes) spent on hygiene and also grooming in the morning by survey respondents.

Determine the 5-number summary and also construct a boxplot for the data offered listed below.

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

Below are 36 sorted ages of an acting award winner.

Find P70 making use of the approach presented in the textbook.

**P70 = 66**

*L = k ÷ 100 x n*

*70 ÷ 100 x 36 = 25.2 (round up)*

*What is the Lth = 2sixth value in the sorted list? 66 *

*What is the next worth in the sorted list? 66 *

*P75 = (66 + 66) ÷ 2 = 66*

IQ scores are measured through a test designed so that the intend is 103 and the standard deviation is 13. Consider the group of IQ scores that are unexplained.

What are the z scores that separate the unusual IQ scores from those that are usual?

What are the IQ scores that separate the unusual IQ scores from those that are usual?(Consider a worth to be unusual if its z score is less than –2 or higher than 2.)

The reduced z score boundary is –2.

The better z score boundary is 2.

The lower bound IQ score is 64.

*(reduced z score x standard deviation) + mean*

The greater bound IQ score is 136.

*(higher z score x traditional deviation) + mean*

If your score on your following statistics test is converted to a z score, which of these z scores would certainly you prefer: –2.00, –1.00, 0, 1.00, 2.00? Why?

The z score of 2.00 is the majority of preferable bereason it is 2.00 standard deviations above the suppose and would correspond to the highest of the five different feasible test scores.

Use the same scale to construct boxplots for the ages of the best actors and also finest actresses from the accompanying information sets.

Use the boxplots to compare the 2 information sets.

*Actors: 27, 37, 43, 50, 76*

*Actresses: 21, 28, 33, 39, 82*

**Although actresses incorporate the oldest age, the boxplot representing actresses reflects that they have actually periods that are mostly lower than those of actors.**

Which is relatively better: a score of 76 on a psychology test or a score of 45 on an economics test? Scores on the psychology test have actually a expect of 89 and also a traditional deviation of 5. Scores on the economics test have actually a suppose of 55 and also a traditional deviation of 7.

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**The business economics test score is relatively better bereason its z score is greater than the z score for the psychology test score.**