Chapter 4 - Summary Statistics
What are three main measures of central location? - correct answer-1) Mean
2) Median
3) Mode
What is a mean? - correct answer-the gravitational center of the distribution
What is a mode? - correct answer-the most frequently occurring value in the data
==> usually only used in large data sets with many repeating values
What is the median? - correct answer-the central value in the order array of the data
Describe the notation for:
1) sample size
2) the variable (i.e. age)
3) the value of individual i for variable X
4) sum of all values - correct answer-1) n
2) X
3) xi <==i is a subscript
4) Capital sigma
What is the "sample mean" ? (2 definitions) - correct answer-1) traditional measure of central
location (of the sample)
2) the balancing point of distribution (see Biostatistics Study Chart and Diagrams)
==> it is the arithmetic average = sum of values and divide by n
What is the notation for the sample mean? Write out the equation. - correct answer-"xbar"
See Biostatistics Study Charts and Diagrams
The value of the mean from a random sample observations can be used to predict the
_________ ____________ - correct answer-population mean
What is the population mean?
==> it is also known as ____ _____? - correct answer-The mean of the true population (what
we are trying to study)
==> expected value
What is the notation for the population mean? Write out the equation. - correct answer-"mu"
See Biostatistics Study Charts and Diagrams
, What is the median? - correct answer-the value with a depth of (n+1)/2
when n is even, averge the two values that straddle a depth of (n+1)/2
EXAM: What must be TRUE in order to calculate the median? - correct answer-the values
must be ORDERED first
Mean vs Median: Why is each one better than the other? When is it best to use each one? -
correct answer-Mean ==> more efficient than the median in describing a distribution's center
b/c it makes use of the quantitative info <== best to use if w/ normal distribution
Median ==> more ROBUST b/c leas influenced by outliers and skews
What is a mode - correct answer-
What is the mode of {4, 6, 7, 8}? Explain. - correct answer-There is no mode b/c none of the
numbers are repeating.
What is the effect on the mean, median, and mode when there is a symmetrical distribution?
- correct answer-mean = median = mode
(not sure on the mode part)
What is the effect on the mean, median, and mode when there is a positive skew? Explain. -
correct answer-mean > median
==> a postive skew means there is a long tail in the postive direction (indicating there is a
positive outlier); the mean is pulled more to the skew
(towards the positive direction) than the median
What is the effect on the mean, median, and mode when there is a negative skew? Explain -
correct answer-mean < median
==> a negative skew means there is a long tail in the negative direction (indicating there is a
negative outlier); the mean is pulled more to the skew
(towards the negative direction) than the median
Which statement is true:
A: the median and mean have the same value, therefore we know that the distribution is
symmetrical
B: the distribution is symmetrical, therefore we know that the median and the mean have the
same value - correct answer-Statement B
we CANNOT guarantee if the distribution is symmetrical just be know that the values of
median and mean have the same value.
What are three main measures of central location? - correct answer-1) Mean
2) Median
3) Mode
What is a mean? - correct answer-the gravitational center of the distribution
What is a mode? - correct answer-the most frequently occurring value in the data
==> usually only used in large data sets with many repeating values
What is the median? - correct answer-the central value in the order array of the data
Describe the notation for:
1) sample size
2) the variable (i.e. age)
3) the value of individual i for variable X
4) sum of all values - correct answer-1) n
2) X
3) xi <==i is a subscript
4) Capital sigma
What is the "sample mean" ? (2 definitions) - correct answer-1) traditional measure of central
location (of the sample)
2) the balancing point of distribution (see Biostatistics Study Chart and Diagrams)
==> it is the arithmetic average = sum of values and divide by n
What is the notation for the sample mean? Write out the equation. - correct answer-"xbar"
See Biostatistics Study Charts and Diagrams
The value of the mean from a random sample observations can be used to predict the
_________ ____________ - correct answer-population mean
What is the population mean?
==> it is also known as ____ _____? - correct answer-The mean of the true population (what
we are trying to study)
==> expected value
What is the notation for the population mean? Write out the equation. - correct answer-"mu"
See Biostatistics Study Charts and Diagrams
, What is the median? - correct answer-the value with a depth of (n+1)/2
when n is even, averge the two values that straddle a depth of (n+1)/2
EXAM: What must be TRUE in order to calculate the median? - correct answer-the values
must be ORDERED first
Mean vs Median: Why is each one better than the other? When is it best to use each one? -
correct answer-Mean ==> more efficient than the median in describing a distribution's center
b/c it makes use of the quantitative info <== best to use if w/ normal distribution
Median ==> more ROBUST b/c leas influenced by outliers and skews
What is a mode - correct answer-
What is the mode of {4, 6, 7, 8}? Explain. - correct answer-There is no mode b/c none of the
numbers are repeating.
What is the effect on the mean, median, and mode when there is a symmetrical distribution?
- correct answer-mean = median = mode
(not sure on the mode part)
What is the effect on the mean, median, and mode when there is a positive skew? Explain. -
correct answer-mean > median
==> a postive skew means there is a long tail in the postive direction (indicating there is a
positive outlier); the mean is pulled more to the skew
(towards the positive direction) than the median
What is the effect on the mean, median, and mode when there is a negative skew? Explain -
correct answer-mean < median
==> a negative skew means there is a long tail in the negative direction (indicating there is a
negative outlier); the mean is pulled more to the skew
(towards the negative direction) than the median
Which statement is true:
A: the median and mean have the same value, therefore we know that the distribution is
symmetrical
B: the distribution is symmetrical, therefore we know that the median and the mean have the
same value - correct answer-Statement B
we CANNOT guarantee if the distribution is symmetrical just be know that the values of
median and mean have the same value.
