STT 215 Practice Exam Questions/Answer Graded A+
2025/2026
Distribution - Tells us what values the variable takes and how often it takes these
values.
Categorical variable - Something that falls into one of several categories. What can be
counted is the count or proportion of individuals in each category.
Example: blood type (A, B, AB, O), hair color, ethnicity
Quantitative (numerical) variable - Something that can be counted or measured for each
individual and then added, subtracted, averaged, etc. across individuals in the
population.
Example: height, age, blood cholesterol level
Quantitative data: discrete versus continous - Discrete if the possible values are isolated
points on the number line.
Continuous if the set of possible values forms an entire interval on the number line.
Ways to represent categorical data - Frequency / Relative Frequency distribution
Bar graph
Pie chart
Ways to represent numerical data - Frequency distribution
Stemplot (stem-and-leaf plot)
Histogram
Ways to represent bivariate numerical data - Scatter plot
Bar graph - Each category is represented by a bar. The bar's height shows the count (or
sometimes the percentage) for that particular category.
Pie chart - Peculiarity: the slices mist represent the parts of one whole (1 or 100%). The
size of a slice depends on what percent of the whole this category represents.
Relative frequency - (frequency) / (number of observations in the data set)
Stemplot - (Also called a stem-and-leaf plot) Each observation is represented by a stem,
consisting of all digits except the final one, which is the leaf.
Work best for small numbers of observations that are all greater than 0.
Display the actual values of the observations.
How to make a stemplot - Separate each observation into a stem (consisting of all but
the final (rightmost) digit), and a leaf (which is that remaining final digit). Stems may
have as many digits as needed, but each leaf contains only a single digit.
, Write the stems in a vertical column with the smallest value at the top, and draw a
vertical line at the right of this column.
Write each lead in the row of its stem, in increasing order out from the stem.
Trimming stems - Trimming numbers means dropping the last digit.
Original data 141, by dropping the last digit, it gives 14.
Splitting stems - If your dataset is of median size, then even when some numbers share
same stem, we separate them into two parts with the same stem, one part with 0-4, and
another part with 5-9.
Histograms - Breaks the range of values of a variable into classes and displays only the
count or percent of the observations that fall into each class.
You can choose any convenient number of classes, but you should always choose
classes of equal width.
Steps to draw a histogram - Divide the range of the data into classes of equal width.
Count the number of individuals in each class. The counts are called frequencies, and a
table of frequencies for all class is a frequency table.
First, on the horizontal axis mark the scale for the variable whose distribution you are
displaying. The vertical axis contains the scale of counts. Each bar represents a class.
The base covers the class. The bar height is the class count.
How to create a histogram: what bin size should you use? - Not too many bins with
either 0 or 1 counts
Not overly summarized that you lose all the information
Not so detailed that it is no longer summary
(Rule of thumb: start with 5 to 10 bins, look at the distribution and refine your bins)
Important property of a density curve is that - areas under the curve correspond to
relative frequencies.
Stemplot versus histograms - Stemplots are quick and dirty histograms that can easily
be done by hand, and therefore are very convenient for back of the envelope
calculations. However, they are rarely found in scientific or laymen publications.
Examining distributions of quantitative variables (stemplots versus histograms) - Once a
graph of the variable is made, we can begin to understand its distribution by looking at
its overall pattern, striking deviations, peaks, gaps, and symmetry / skewness.
Shape, center, and spread (or variation).
Modes - One or several peaks.
If unique major peak, then call unimodal.
Center/midpoint - The value with roughly half the observations taking smaller values
and half taking larger values.
2025/2026
Distribution - Tells us what values the variable takes and how often it takes these
values.
Categorical variable - Something that falls into one of several categories. What can be
counted is the count or proportion of individuals in each category.
Example: blood type (A, B, AB, O), hair color, ethnicity
Quantitative (numerical) variable - Something that can be counted or measured for each
individual and then added, subtracted, averaged, etc. across individuals in the
population.
Example: height, age, blood cholesterol level
Quantitative data: discrete versus continous - Discrete if the possible values are isolated
points on the number line.
Continuous if the set of possible values forms an entire interval on the number line.
Ways to represent categorical data - Frequency / Relative Frequency distribution
Bar graph
Pie chart
Ways to represent numerical data - Frequency distribution
Stemplot (stem-and-leaf plot)
Histogram
Ways to represent bivariate numerical data - Scatter plot
Bar graph - Each category is represented by a bar. The bar's height shows the count (or
sometimes the percentage) for that particular category.
Pie chart - Peculiarity: the slices mist represent the parts of one whole (1 or 100%). The
size of a slice depends on what percent of the whole this category represents.
Relative frequency - (frequency) / (number of observations in the data set)
Stemplot - (Also called a stem-and-leaf plot) Each observation is represented by a stem,
consisting of all digits except the final one, which is the leaf.
Work best for small numbers of observations that are all greater than 0.
Display the actual values of the observations.
How to make a stemplot - Separate each observation into a stem (consisting of all but
the final (rightmost) digit), and a leaf (which is that remaining final digit). Stems may
have as many digits as needed, but each leaf contains only a single digit.
, Write the stems in a vertical column with the smallest value at the top, and draw a
vertical line at the right of this column.
Write each lead in the row of its stem, in increasing order out from the stem.
Trimming stems - Trimming numbers means dropping the last digit.
Original data 141, by dropping the last digit, it gives 14.
Splitting stems - If your dataset is of median size, then even when some numbers share
same stem, we separate them into two parts with the same stem, one part with 0-4, and
another part with 5-9.
Histograms - Breaks the range of values of a variable into classes and displays only the
count or percent of the observations that fall into each class.
You can choose any convenient number of classes, but you should always choose
classes of equal width.
Steps to draw a histogram - Divide the range of the data into classes of equal width.
Count the number of individuals in each class. The counts are called frequencies, and a
table of frequencies for all class is a frequency table.
First, on the horizontal axis mark the scale for the variable whose distribution you are
displaying. The vertical axis contains the scale of counts. Each bar represents a class.
The base covers the class. The bar height is the class count.
How to create a histogram: what bin size should you use? - Not too many bins with
either 0 or 1 counts
Not overly summarized that you lose all the information
Not so detailed that it is no longer summary
(Rule of thumb: start with 5 to 10 bins, look at the distribution and refine your bins)
Important property of a density curve is that - areas under the curve correspond to
relative frequencies.
Stemplot versus histograms - Stemplots are quick and dirty histograms that can easily
be done by hand, and therefore are very convenient for back of the envelope
calculations. However, they are rarely found in scientific or laymen publications.
Examining distributions of quantitative variables (stemplots versus histograms) - Once a
graph of the variable is made, we can begin to understand its distribution by looking at
its overall pattern, striking deviations, peaks, gaps, and symmetry / skewness.
Shape, center, and spread (or variation).
Modes - One or several peaks.
If unique major peak, then call unimodal.
Center/midpoint - The value with roughly half the observations taking smaller values
and half taking larger values.
