Chapter 5: measures of dispersion in business

If the standard deviation is 10, the mean is 50, and the value in question is 30, then what is the Z-score?

-2

If the standard deviation is 5, the mean is 40, and the value in question is 45, then what is the Z-score?

1

Find the range for one standard deviation in the following data set: 16, 20, 14, 24, 16, 19, 30, and 8

12.175 to 24.575

Find the standard deviation for the following data set: 101, 106, 125, 142, 78, and 109

19.9

Which of these would have the largest area?

2

There are 30 students in Alice's math class. If the students' marks on the last test exhibit a normal distribution, and the average grade was 75%, then how many students scored within one standard deviation of 75%?

20

Find the variance for the following data set: (rounding the answer to the nearest tenth). 16, 20, 14, 24, 16, 19, 30, and 8

38.5

Find the variance for the following data set: 101, 106, 125, 142, 78, and 109

395

Find the standard deviation for the following data set: 16, 20, 14, 24, 16, 19, 30, and 8

6.2

_____ of normally distributed data is always contained within 1 standard deviation of the mean.

68%

What percentage of the data is within two standard deviations to the left and right of the middle of a graph with a normal distribution?

95%

_____ of normally distributed data is always contained within 2 standard deviations of the mean.

95%

What percentage of the data is within three standard deviations to the left and right of the middle of a graph with a normal distribution?

99.7%

_____ of normally distributed data is always contained within 3 standard deviations of the mean.

99.7%

What is standard deviation?

A measure of how scattered a data set is.

Variance provides a measurement of what general data attribute?

Data variability

What limiting factor does the average of a data set present?

Does not indicate how numbers vary from the mean

Professor Dublin wants to ensure he is thorough in his review of student performance, so he decides to calculate 'standard deviation' as well. What must Professor Dublin do to figure out this measure of variability?

Identify how far from average each score is.

What is the variance that would be calculated from 5 data points that all had the same value?

It would equal zero

Negative Z-scores appear on the _____ side of the normal distribution.

Left

Where is the normal distribution curve at its highest point?

Mean

Which side of the normal distribution does the positive Z-score appear on?

Right

Which of the following Excel functions will give you the variance of the population as a whole, versus individual elements?

STDEV.S

What is the difference between variance computed for sampled data and full population data?

Sampled data always has a larger variance calculation

Professor Dublin has just given a biology exam and wants to calculate the 'range' of performance of his students. What must he do?

Subtract the lowest score from the highest score.

What attribute of data is quantified using Chebyshev's inequality?

The dispersion or spread of a data distribution

Which of the following is a fixed or discrete data point, rather than continuous? Jet fuel prices The number of checked bags on flight 329 Personnel costs year-over-year Cost of an airline ticket

The number of checked bags on flight 329

The mean of a graph with a normal distribution is located where?

The tip of the curve

In recent versions of Excel (2010 and higher), which function should you use to calculate variance for a set of data?

VAR.S

The function STANDARDIZE requires which three data elements?

Value, mean, standard deviation

What is the mathematical definition of statistical variance?

Variance is the average of squared differences from the mean

'Variance' is similar to 'standard deviation' in all the following ways EXCEPT: With variance, you do NOT square the deviation. With variance, you do NOT take the square root of standard deviation. With variance, you do NOT sum up the squared deviations. With variance, you do NOT calculate the average. With variance, you do NOT calculate the score minus the average.

With variance, you do NOT take the square root of standard deviation.

Data can be described as being _____ when it is dynamic and changes frequently.

continuous

a numerical value to represent the variability of the population.

parameter

'Variance' attempts to estimate

the parameter.

If you needed to know how individual sales values compare against the average sales and the standard deviation, which measure will you use?

z-score

Which has the lowest area under it?

-3

that no more than 1 / k2 of the distribution's values will be more than k standard deviations away from the mean

Chebyshev's inequality

What values are required to calculate Chebyshev's inequality?

The mean and standard deviation

Range, standard deviation, and variance are 'similar' in that each looks at

how spread out the data is.

When calculated for a normal distribution, how do the values for Chebyshev's theorem compare to the 68-95-99.7 rule of thumb?

Chebyshev's inequality provides a less precise percentage

What attribute is measured by an analysis of the variance found in yearly investment returns?

Risk

What is a Z-score?

A measurement of the distance from the mean to a point in terms of standard deviations.

In a business context, normally distributed data can be used to accomplish all of the following EXCEPT: Assess market conditions Manage price or cost volatility Determine the mission of an organization Mitigate risk

Determine the mission of an organization

What type of data distribution is not appropriate to use with Chebyshev's inequality?

It is usable for all data distributions

The left and right sides of a graph with a normal distribution have what characteristic?

They are mirror images of each other.

A statistician has figured out the percentage of the area under a normal curve that meets certain criteria. How would they apply this knowledge to a given sample?

They would multiply the percentage by the total sample size.

In a normal distribution, Six Sigma seeks to limit errors to occur only outside of _____ standard deviations.

Three

A statistician is studying a normally distributed population, and they are interested in the data that falls from the mean to one standard deviation above the mean. What percentage of the population falls within this range?

34%

Using Chebyshev's inequality, what minimal percentage of values will lie within 2 standard deviations of the mean?

75%

'Variance' is similar to 'standard deviation' in all the following ways EXCEPT:

With variance, you do NOT take the square root of standard deviation.