UCF QMB 3200 LATEST STUDY EXAMS GUIDED
QUESTIONS AND ANSWERS SURE A+
✔✔Distribution Shape - ✔✔is measured by skewness.
If the shape of the data is skewed to the left, the skewness
is negative;
if to the right then skewness is positive;
and if the data is symmetric, then skewness is zero.
For a symmetric distribution, the mean and median
are equal.
For a positively skewed distribution, the
mean is usually greater than the median and a
negatively skewed distribution, the mean is usually
less than the median.
✔✔How would we calculate skewness in excel? - ✔✔=SKEW
✔✔Z scores - ✔✔The z-Score yields a standardized value and is the
number of standard deviations from the mean.
,The z-Score for any observation is a measure of the
relative location of the observation in the dataset.
Measures the relative location of values in the
dataset. This helps determine how far a particular
value is from the mean. z-Scores use the mean and
standard deviation in its calculation.
✔✔Chebyshev's Theorem - ✔✔Allows us to make statements about the population
of the data values that must be within a specified
number of standard deviations from the mean.
At least (1 −1/ 𝑧^2) of the data values must be within
z standard deviations of the mean (z > 1).
It applies to any dataset.
If the data is bell shaped around the mean, we know
Approx. 68% of the data is within one s of ̅ 𝑥.
Approx. 95% of the data is within two s of ̅ 𝑥.
Approx. 99.7% of the data is within three s of ̅ 𝑥.
✔✔Outliers - ✔✔are extreme values relative to the rest of
the data. z-Score can help identify outliers.
Typically, any z-Score greater than 3 is an
outlier.
Alternatively, we can use the interquartile range,
where the:
lower limit: 𝑄1 − 1.5(𝐼𝑄R)
upper limit: 𝑄3 + 1.5(𝐼Qr)
✔✔Covariance - ✔✔is a descriptive measure of the linear
association between two variables.
If Covariance or s sub-xy> 0, then there is a positive linear association between x and y.
If sxy < 0, then there is a negative linear association between x and y.
Be careful about attributing the size of the covariance and the strength of the linear
relationship because covariance depends on the units of measurement.
✔✔correlation coefficient - ✔✔The sample correlation coefficient ranges from -1 to
+1. If it is exactly 1 (perfect positive linear
relationship), then all the data would be on a
positively sloped line; and if it is exactly -1 (perfect
negative linear relationship), then all the data would
be on a negatively sloped line.
, As the data deviates from the slope of the line, the correlation coefficient moves closer
to zero.
✔✔How would we calculate covariance of a sample in excel? - ✔✔=covariance.s
✔✔How would we calculate the Correlation Coefficient in excel? - ✔✔=correl(
✔✔Probability - ✔✔A numerical measure of the likelihood of an event
occurring. A probability ranges from 0 to 1, such as
the probability it will rain tomorrow.
✔✔experiment - ✔✔Is a process generating well-defined outcomes.
Rolling a 6-sided die results in six possible outcomes:
S = {1, 2, 3, 4, 5, 6}
✔✔Counting rules for experiments - ✔✔If an experiment has k steps with n1 possible
outcomes on step 1, n 2 possible outcomes on step 2,
and so on, then the total number of experimental
outcomes is (n1 )(n2 )...(nk ).
Thus, tossing a coin 6 times yields: (2)(2)(2)(2)(2)(2) =
64.
✔✔Permutations - ✔✔a counting rule computing the number of
experimental outcomes when n objects are to be
selected from a set of N objects where the order of
selections is important.
✔✔Assigning Probabilities requirements - ✔✔1. The probability assigned to each
experimental
outcome must be between 0 and 1, inclusively
2. The sum of the probabilities for all experimental outcomes must be equal to 1.
✔✔Three methods to assign probability: - ✔✔1. Classical Method - such as a coin toss
or a roll of a
6-sided die.
2. Relative Frequency Method: is used when data are
available to estimate the proportion of time the experimental outcome will occur if the
experiment is
repeated a large number of times.
3. Subjective Method: is used when outcomes are not
equally likely and data is unavailable.
QUESTIONS AND ANSWERS SURE A+
✔✔Distribution Shape - ✔✔is measured by skewness.
If the shape of the data is skewed to the left, the skewness
is negative;
if to the right then skewness is positive;
and if the data is symmetric, then skewness is zero.
For a symmetric distribution, the mean and median
are equal.
For a positively skewed distribution, the
mean is usually greater than the median and a
negatively skewed distribution, the mean is usually
less than the median.
✔✔How would we calculate skewness in excel? - ✔✔=SKEW
✔✔Z scores - ✔✔The z-Score yields a standardized value and is the
number of standard deviations from the mean.
,The z-Score for any observation is a measure of the
relative location of the observation in the dataset.
Measures the relative location of values in the
dataset. This helps determine how far a particular
value is from the mean. z-Scores use the mean and
standard deviation in its calculation.
✔✔Chebyshev's Theorem - ✔✔Allows us to make statements about the population
of the data values that must be within a specified
number of standard deviations from the mean.
At least (1 −1/ 𝑧^2) of the data values must be within
z standard deviations of the mean (z > 1).
It applies to any dataset.
If the data is bell shaped around the mean, we know
Approx. 68% of the data is within one s of ̅ 𝑥.
Approx. 95% of the data is within two s of ̅ 𝑥.
Approx. 99.7% of the data is within three s of ̅ 𝑥.
✔✔Outliers - ✔✔are extreme values relative to the rest of
the data. z-Score can help identify outliers.
Typically, any z-Score greater than 3 is an
outlier.
Alternatively, we can use the interquartile range,
where the:
lower limit: 𝑄1 − 1.5(𝐼𝑄R)
upper limit: 𝑄3 + 1.5(𝐼Qr)
✔✔Covariance - ✔✔is a descriptive measure of the linear
association between two variables.
If Covariance or s sub-xy> 0, then there is a positive linear association between x and y.
If sxy < 0, then there is a negative linear association between x and y.
Be careful about attributing the size of the covariance and the strength of the linear
relationship because covariance depends on the units of measurement.
✔✔correlation coefficient - ✔✔The sample correlation coefficient ranges from -1 to
+1. If it is exactly 1 (perfect positive linear
relationship), then all the data would be on a
positively sloped line; and if it is exactly -1 (perfect
negative linear relationship), then all the data would
be on a negatively sloped line.
, As the data deviates from the slope of the line, the correlation coefficient moves closer
to zero.
✔✔How would we calculate covariance of a sample in excel? - ✔✔=covariance.s
✔✔How would we calculate the Correlation Coefficient in excel? - ✔✔=correl(
✔✔Probability - ✔✔A numerical measure of the likelihood of an event
occurring. A probability ranges from 0 to 1, such as
the probability it will rain tomorrow.
✔✔experiment - ✔✔Is a process generating well-defined outcomes.
Rolling a 6-sided die results in six possible outcomes:
S = {1, 2, 3, 4, 5, 6}
✔✔Counting rules for experiments - ✔✔If an experiment has k steps with n1 possible
outcomes on step 1, n 2 possible outcomes on step 2,
and so on, then the total number of experimental
outcomes is (n1 )(n2 )...(nk ).
Thus, tossing a coin 6 times yields: (2)(2)(2)(2)(2)(2) =
64.
✔✔Permutations - ✔✔a counting rule computing the number of
experimental outcomes when n objects are to be
selected from a set of N objects where the order of
selections is important.
✔✔Assigning Probabilities requirements - ✔✔1. The probability assigned to each
experimental
outcome must be between 0 and 1, inclusively
2. The sum of the probabilities for all experimental outcomes must be equal to 1.
✔✔Three methods to assign probability: - ✔✔1. Classical Method - such as a coin toss
or a roll of a
6-sided die.
2. Relative Frequency Method: is used when data are
available to estimate the proportion of time the experimental outcome will occur if the
experiment is
repeated a large number of times.
3. Subjective Method: is used when outcomes are not
equally likely and data is unavailable.
