Practice Questions 2.3

What information about a data value is given by its deviation?

A) The statistical distance and direction from the mean.
B)  The magnitude (absolute value) of the difference between the data value and the median.
C) The mathematical distance and direction from the mean.
D)  How different the data value is from the mean and median.

In statistics, a deviation applies to only one data value.

True
False
True False

Variance (σ2) is what type of measure of spread?

A)  A measure of spread standardized for the number of data values.
B)  A measure of spread normalized for shape.
C)  A measure of spread adjusted for bias.
D)  A raw measure of spread.

Does the sum of squares (SS) usually get bigger as more data values are added to the data set?

A)  Yes, because bigger data sets must have bigger sum of squares than smaller data sets.
B)  No, because the sum of squares is adjusted for the number of data values in the data set.
C)  No, because the new data values could have negative squares.
D)  Yes, because there are more numbers in the data set to sum.

What is the appropriate denotation for standard deviation?

A)  s population, σ for sample.
B)  µ for population, s for sample 
C)  σ for population, s for sample.
D)  σ for population, std for sample. 

What is the appropriate denotation for variance?

A)  μ2 for population, s2 for sample
B)  σ2 for population, s2 for sample
C)  φ¯ for population, v¯ for sample
D)  VAR for population, var for sample

To calculate variance, statistics does not average the deviations, instead it averages the?

A)  The positive and negative deviations separately.
B)  The square-root of the squared deviations. 
C)  The absolute value of the deviations.
D)  Squared deviations.

Match the appropriate set of statistics to the descriptions below.

__ Extract the most information from a column of data.
__ Less affected by extreme values.


A.  Resistant statistics.
B.  Efficient statistics.

What is the statistical term for all the squared deviations added together?

A) Root mean square
B) Standard Deviation
C) Sum of squares
D) Variance

Is the average deviation better than the standard deviation (σ)?

A)  No, because the average deviation always equals zero.
B)  No, because the standard deviation is a standardized version of the average deviation.
C)  Yes, because the average is the most representative value. 
D)  Yes, because the average deviation is much quicker to calculate and much easier to use.

A data value close to the mean has a?

A) Middle deviation
B) No deviation
C) Large deviation
D) Small deviation

The mean (µ) is used when thinking about the data values in a column of data because? (select two of the answers below)

A) The mean is easier to calculate than the median.
B) The mean can be used in advanced statistical methods.
C) A single number is easy to think about. 
D) The mean best represents the values in the column of data.

Can the standard deviation (σ) be used to find probability?

A)  No, because spread is not needed to find probability.
B)  Yes, it can with a normal curve. 
C)  No, because the average deviation is used. 
D)  Yes, because it is part of a distribution. 

Does the average deviation always equal zero for every data set?

A)  Yes, because the deviations cluster about the mean.
B) Yes, because the positive and negative deviation cancel each other.
C) No, because the average deviation equals zero for some data sets, but not for all datasets.
D) No, because this is not true.

A deviation can never equal zero

True
False
True False

A data value less than the mean has a?

A) Positive deviation
B) Left deviation
C) Negative deviation
D) None of the above

The sum of squares (SS) is what type of measure spread?

A)  A normalized measure of spread.
B)  A raw measure of spread.
C)  An adjusted measure of spread.
D) A standardized measure of spread.

Match the appropriate statistic for a distribution of efficient statistics.

__ Shape
__ Location
__ Spread

A. Mean
B. Histogram
C. Standard deviation

How is the sum of squares (SS) standardized into variance (σ2)?

A)  Divide by the degrees of freedom.
B)  Sum of squares is the same value as the variance.
C)  Take the square-root of the sum of squares.
D) Divide by the number of data values.

The mean (µ) is NOT needed to calculate a deviation

True
False
True False

Two data sets have the same size, but Data set A has a sum of squares of 97 and Data set B has a sum of squares of 197. In which data set are the data values more widely spread out?

A)  Data set B, because 197 can have more variation than 97.
B) Data set A, because 97 is closer to zero than 197. 
C) Data set A, because a sum of squares of 97 is smaller than a sum of squares of 197.
D) Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97.

A bigger standard deviation for a data set means the data values are?

A) Spread wider apart.
B) Spread narrower together.
C) Spread more evenly about the mean.
D) Have a more symmetrical spread.

What is the formula for the sum of squares (SS)?

A) Sum of squares= (x - xbar)
B) Sum of squares = ∑(x−xbar)²
C) Sum of squares= ∑(x)²-∑(xbar)²
D) Sum of squares= (x - xbar)²

Which one of the following answers is NOT correct about standard deviation?

A)  Standard deviation= √variance
B) Standard deviation= √o²
C)  Standard deviation²= Variance^-
D)  Standard deviation= Variance²

The efficient measure of spread for a column of data is the?

A) Standard deviation.
B) Average deviation.
C) The average of all the deviation in the data set.
D) Middle deviation.