Portage Math 110 Elementary Statistics (Module 2)
frequency distribution - ✔✔ANSW✔✔..A tabular summary of data showing the number (frequency) of
observations in each of several distinctive (nonoverlapping) categories or classes.
relative frequency - ✔✔ANSW✔✔..A ratio that compares the frequency of each category to the total.
frequency of the class / n where n = total count of all classes
relative percentage - ✔✔ANSW✔✔..percentage of time the value occurs in the sample or population
relative frequency x 100
charting - ✔✔ANSW✔✔..a means to represent frequencies visually
column chart - ✔✔ANSW✔✔..Data graphed as a series of vertical bars
x-axis: class
y-axis: frequency of class
bar chart - ✔✔ANSW✔✔..Data graphed as a series of horizontal bars
,x-axis: frequency of class
y-axis: class
pie chart - ✔✔ANSW✔✔..a chart that shows the relationship of a part to a whole
best suited for the distributions focused on the proportions
3 step method to group numerical data into classes - ✔✔ANSW✔✔..1. determine the number of classes
to be evaluated
2. determine the width of each class
3. determine the limits of each class
Number of classes - ✔✔ANSW✔✔..(usu b/w 5 and 20)
less than 25 > 5 to 6
25 to 50 > 7 to 14
More than 50 > 15-20
Width of class - ✔✔ANSW✔✔..approx width =
(largest data value - smallest data value) / # of classes
qualitative data - ✔✔ANSW✔✔..frequency distributions
relative frequency distributions
percent frequency distributions
Graphical: bar, column, pie charts
quantitative data - ✔✔ANSW✔✔..frequency distributions
relative frequency distributions
percent frequency distributions
Graphical: histograms
,positive relationship - ✔✔ANSW✔✔..an association between two variables in which they increase or
decrease together
negative relationship - ✔✔ANSW✔✔..an association between two variables in which one increases while
the other decreases
no relationship - ✔✔ANSW✔✔..as one variable increases the other stays the same
measures of central tendency - ✔✔ANSW✔✔..mean, median, mode
"typical" or "average" value of a data set
sample mean - ✔✔ANSW✔✔..x bar
the arithmetic average value of the responses on a variable (sum of values / number of observations)
population mean - ✔✔ANSW✔✔..μ (mu)
calculated mean of the entire population (sum of values in population / N = number of observations in
pop)
median - ✔✔ANSW✔✔..midpoint
the middle score in a distribution; half the scores are above it and half are below it
odd = middle number
even = average of two middle numbers
mode - ✔✔ANSW✔✔..The value that occurs most frequently in a given data set.
percentile - ✔✔ANSW✔✔..Specific point in a distribution of data that has a given percentage of cases
below it.
quartile - ✔✔ANSW✔✔..A division of the total into four intervals, each one representing one-fourth of
the total.
, median is Q2
median of lower half is Q1
median of upper half is Q3
interquartile range - ✔✔ANSW✔✔..The difference between the upper and lower quartiles.
Q3-Q1
population variance - ✔✔ANSW✔✔..the difference between each data point in a data set and the
population mean of the data set
N, number in the population
sample variance - ✔✔ANSW✔✔..the difference between each data point in a data set and the sample
mean of the data set
n, which is the number in the sample
deviation about the mean - ✔✔ANSW✔✔..calculated difference between the data value and the mean
sample standard deviation - ✔✔ANSW✔✔..the positive square root of the variance
population standard deviation - ✔✔ANSW✔✔..the square root of the population variance
coefficient of variation - ✔✔ANSW✔✔..Standard deviation / mean x 100
(expressed as percentage)
how the size of the standard deviation compares to the mean of the data set
z-score - ✔✔ANSW✔✔..the number of standard deviations a particular score is from the mean
empirical rule (bell curve) - ✔✔ANSW✔✔..68.27 - 95.45 - 99.73
frequency distribution - ✔✔ANSW✔✔..A tabular summary of data showing the number (frequency) of
observations in each of several distinctive (nonoverlapping) categories or classes.
relative frequency - ✔✔ANSW✔✔..A ratio that compares the frequency of each category to the total.
frequency of the class / n where n = total count of all classes
relative percentage - ✔✔ANSW✔✔..percentage of time the value occurs in the sample or population
relative frequency x 100
charting - ✔✔ANSW✔✔..a means to represent frequencies visually
column chart - ✔✔ANSW✔✔..Data graphed as a series of vertical bars
x-axis: class
y-axis: frequency of class
bar chart - ✔✔ANSW✔✔..Data graphed as a series of horizontal bars
,x-axis: frequency of class
y-axis: class
pie chart - ✔✔ANSW✔✔..a chart that shows the relationship of a part to a whole
best suited for the distributions focused on the proportions
3 step method to group numerical data into classes - ✔✔ANSW✔✔..1. determine the number of classes
to be evaluated
2. determine the width of each class
3. determine the limits of each class
Number of classes - ✔✔ANSW✔✔..(usu b/w 5 and 20)
less than 25 > 5 to 6
25 to 50 > 7 to 14
More than 50 > 15-20
Width of class - ✔✔ANSW✔✔..approx width =
(largest data value - smallest data value) / # of classes
qualitative data - ✔✔ANSW✔✔..frequency distributions
relative frequency distributions
percent frequency distributions
Graphical: bar, column, pie charts
quantitative data - ✔✔ANSW✔✔..frequency distributions
relative frequency distributions
percent frequency distributions
Graphical: histograms
,positive relationship - ✔✔ANSW✔✔..an association between two variables in which they increase or
decrease together
negative relationship - ✔✔ANSW✔✔..an association between two variables in which one increases while
the other decreases
no relationship - ✔✔ANSW✔✔..as one variable increases the other stays the same
measures of central tendency - ✔✔ANSW✔✔..mean, median, mode
"typical" or "average" value of a data set
sample mean - ✔✔ANSW✔✔..x bar
the arithmetic average value of the responses on a variable (sum of values / number of observations)
population mean - ✔✔ANSW✔✔..μ (mu)
calculated mean of the entire population (sum of values in population / N = number of observations in
pop)
median - ✔✔ANSW✔✔..midpoint
the middle score in a distribution; half the scores are above it and half are below it
odd = middle number
even = average of two middle numbers
mode - ✔✔ANSW✔✔..The value that occurs most frequently in a given data set.
percentile - ✔✔ANSW✔✔..Specific point in a distribution of data that has a given percentage of cases
below it.
quartile - ✔✔ANSW✔✔..A division of the total into four intervals, each one representing one-fourth of
the total.
, median is Q2
median of lower half is Q1
median of upper half is Q3
interquartile range - ✔✔ANSW✔✔..The difference between the upper and lower quartiles.
Q3-Q1
population variance - ✔✔ANSW✔✔..the difference between each data point in a data set and the
population mean of the data set
N, number in the population
sample variance - ✔✔ANSW✔✔..the difference between each data point in a data set and the sample
mean of the data set
n, which is the number in the sample
deviation about the mean - ✔✔ANSW✔✔..calculated difference between the data value and the mean
sample standard deviation - ✔✔ANSW✔✔..the positive square root of the variance
population standard deviation - ✔✔ANSW✔✔..the square root of the population variance
coefficient of variation - ✔✔ANSW✔✔..Standard deviation / mean x 100
(expressed as percentage)
how the size of the standard deviation compares to the mean of the data set
z-score - ✔✔ANSW✔✔..the number of standard deviations a particular score is from the mean
empirical rule (bell curve) - ✔✔ANSW✔✔..68.27 - 95.45 - 99.73
