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AP Statistics Exam Review Detailed Questions And Expert Answers
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AP Statistics Exam Review Detailed QuestionsAnd Expert Answers
What is a dotplot?
A graphical display which shows "dots" for each point. It's good for categorical
data- ie data classified into categories.
What's the difference between categorical and quantitative data?
Categorical data fits into various categories; whereas, quantitative data has
numerical values associated with it.
What is a bar chart?
A display for categorical data which indicates frequencies or percents for each
category.
What are histograms?
Histograms are good for large quantitative data sets- either having numbers at the
left/right of a bar to show the amount of data in-between each value or in the
center of a bar to show the amount of data at a certain value. Sometimes, the axis
will just be the frequency, but often, it can be the relative frequency (ie.
amount/total).
What do relative areas in histograms mean?
Relative areas correspond to relative frequencies (ie. if 10% of the area for a
histogram is between 25-26, that means that 10% of the data falls between 25 and
26.
What's a stemplot/stem and leaf plot?
It has stems which are some digit and leaves which are the other part of the
number (for example depending on context 5|7 could be 57, 5.7, or some other
,variant- that's why a key must always be included). It's good for looking at
individual data in small data sets.
What is important in analyzing visual data displays?
SOCS (Shape, Outlier, Center, Spread):
Shape-How is the data shaped (skewed left/right, symmetric, bimodal, etc.)? Are
there any clusters (subgroups which the data falls into)? Are there any gaps in the
data set?
Outliers: Are there any outliers within the data set?
Center: Give the mean/median- the value which is the approximate midpoint of
the data
Spread- What is the range OR IQR (if it's easy to find) of the data set?
What is a mode? How do modes relate to unimodal/bimodal data sets?
A mode is a major peak in the data (most repeated value). A unimodal data set has
just one mode; whereas, a bimodal data set has two modes.
What are some possible descriptions of shapes within distributions?
Symmetric- There is a vertical line of symmetry, splitting the graph into two equal
parts.
Skewed Right- Data decreases for higher values/has less area for higher values
Skewed Left- Data slopes upwards from the left (less area for lower values).
Bell shaped- symmetric with a center mound and tails going to the left/right.
Uniform- Straight line across/data distribution stays constant.
,What is a cumulative relative frequency plot (or ogive), and how does it relate to
skewness?
A CRF plot shows the percentage of data accumulated along the y axis by each
value of the data along the x. For instance, (10,0.15) would mean that 15% of the
data is less than or equal to 10.
A distribution skewed to the left has a frequency plot which rises slowly at first and
steeply later; whereas, a distributions skewed to the right has a relative frequency
plot rising quickly at first and then slowing down later.
What's the difference between descriptive statistics and statistical analysis?
Descriptive statistics means summarizing averages, shape of a distribution, etc.
while statistical analysis means drawing inferences from limited data.
What are the two main ways of measuring center?
The median (the middle number of a set when arranged in order).
The mean (summing the values in a set and dividing by the number of quantities in
that set)
When does it make more sense to use the median over the mean?
When there are outliers which we want to minimize. We say the median is
RESISTANT to outliers (which means it's not affected).
What are the notations for mean of a population and mean of a sample?
The sample mean usually assumes a simple random sample. The mean is
computed by ∑x/n.
, What are the ways of describing variability/dispersion of the measurements?
1) Range - difference between largest and smallest values.
2) IQR- difference between largest and smallest values after removing lower and
upper quarters.
There are two ways of computing this : way 1) simply take out upper and lower
quarters of the data and subtract.
2) Find Q1 by taking the median of the lower half and Q3 by the median of the
upper half (median itself must be included if there are an odd number of points).
Then do Q3-Q1 to get the IQR. These should be equivalent if there are many data
points.
3) Variance- an average of squared distances from the mean
4) Standard deviation- square root of the variance
What is the rule for designating outliers?
Outliers are considered to be any value above Q3+1.5IQR
OR
any value below Q1-1.5IQR
How is the variance calculated for a population?How is it calculated for a sample?
So for a population you sum up all of the squares of the deviations from the mean
and divide by the number of terms. You do the same thing for a sample but divide
by number of terms-1 due to degrees of freedom.
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