STUDY.COM BUS 212-CHAPTER 5
What is a Z-score?
A measurement of the distance from the mean to a point in terms of standard deviations.
Variance provides a measurement of what general data attribute?
Data variability
'Variance' attempts to estimate
The parameter
The mean of a graph with a normal distribution is located where?
The tip of the curve
In a normal distribution, Six Sigma seeks to limit errors to occur only outside of _____ standard deviations.
Three
When plotted data points fall primarily inside the boundaries of this chart (sometimes called a bell curve), it is indicative that the data can be characterized as _____.
normally distributed data
If the standard deviation is 5, the mean is 40, and the value in question is 45, then what is the Z-score?
1
Range, standard deviation, and variance are 'similar' in that each looks at
how spread out the data is.
Where is the normal distribution curve at its highest point?
Mean
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
_____ of normally distributed data is always contained within 1 standard deviation of the mean.
68%
In recent versions of Excel (2010 and higher), which function should you use to calculate variance for a set of data?
VAR.S
'Variance' is similar to 'standard deviation' in all the following ways EXCEPT:
With variance, you do NOT take the square root of standard deviation.
What values are required to calculate Chebyshev's inequality?
The mean and standard deviation
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
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?
The number of checked bags on flight 329
If the standard deviation is 10, the mean is 50, and the value in question is 30, then what is the Z-score?
-2
Find the standard deviation for the following data set: 16, 20, 14, 24, 16, 19, 30, and 8
6.28
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
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.
Which statement about these two datapoints is TRUE?
A is normally distributed, and B is an outlier.
What is the mathematical definition of statistical variance?
Variance is the average of squared differences from the mean
What is standard deviation?
A measure of how scattered a data set is.
Data can be described as being _____ when it is dynamic and changes frequently.
continuous
Using Chebyshev's inequality, what minimal percentage of values will lie within 2 standard deviations of the mean?
75%
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 is the variance that would be calculated from 5 data points that all had the same value?
It would equal zero
What attribute is measured by an analysis of the variance found in yearly investment returns?
Risk
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.
Which of these would have the largest area?
Everything under a Z-score of 2
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%
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%
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
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 limiting factor does the average of a data set present?
Does not indicate how numbers vary from the mean
Negative Z-scores appear on the _____ side of the normal distribution.
Left
Which side of the normal distribution does the positive Z-score appear on?
Right
The function STANDARDIZE requires which three data elements?
Value, mean, standard deviation
Which has the lowest area under it?
Z-score of -3
Find the variance for the following data set: 101, 106, 125, 142, 78, and 109
395
_____ of normally distributed data is always contained within 3 standard deviations of the mean.
99.7%
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 (round intermediate calculations to the nearest whole number).
19.6
In a business context, normally distributed data can be used to accomplish all of the following EXCEPT:
Determine the mission of an organization
