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# AP Statistics Unit 1 Test With Answers

AP Statistics Unit 1 Test

Individuals
objects described by a set of data
Variable
any characteristic of an individual
Categorical Variable
places an individual into one of several groups or categories
Quantitative Variable
takes numerical values for which it makes sense to find an average
Distribution
tells us what values a variable takes and how often it takes those values
two-way table
describes two categorical variables, organizing counts according to a row variable and a column variable
marginal distribution
the distribution of values of that variable among all individuals described by the table (for a two-way table)
How to examine a marginal distribution

1) Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals.

2) Make a graph to display the marginal distribution.

conditional distribution
describes the values of that variable among individuals who have a specific value of another variable
How to examine or compare conditional distributions

1) Select the row(s) or column(s) of interest.

2) Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s).

3) Make a graph to display the conditional distribution.
– Use a side-by-side bar graph or segmented bar graph to compare distributions.

How to make a dotplot

1) Draw a horizontal axis (a number line) and label it with the variable name.

2) Scale the axis from the minimum to the maximum value.

3) Mark a dot above the location on the horizontal axis corresponding to each data value.

How to Examine the Distribution of a Quantitative Variable

1) In any graph, look for the overall pattern and for striking departures from that pattern.

2) Describe the overall pattern of a distribution by its:
Shape
Center

3) Note individual values that fall outside the overall pattern. These departures are called outliers.

symmetric
the right and left sides of the graph are approximately mirror images of each other
skewed to the right (right-skewed)
the right side of the graph (containing the half of the observations with larger values) is much longer than the left side
skewed to the left (left-skewed)
the left side of the graph is much longer than the right side
How to make a stemplot
1) Separate each observation into a stem (all but the final digit) and a leaf (the final digit).
2) Write all possible stems from the smallest to the largest in a vertical column and draw a vertical line to the right of the column.
3) Write each leaf in the row to the right of its stem.
4) Arrange the leaves in increasing order out from the stem.
5) Provide a key that explains in context what the stems and leaves represent.
The most common graph of the distribution of one quantitative variable is a…
histogram
How to make a histogram
1) Divide the range of data into classes of equal width.
2) Find the count (frequency) or percent (relative frequency) of individuals in each class.
3) Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals.
median
the midpoint of a distribution
IQR
Q3 – Q1
To calculate the quartiles:
1) Arrange the observations in increasing order and locate the median.
2) The first quartile Q1 is the median of the observations located to the left of the median in the ordered list.
3) The third quartile Q3 is the median of the observations located to the right of the median in the ordered list.
Rule for Outliers
Call an observation an outlier if it falls more than 1.5 x IQR above the third quartile or below the first quartile
five-number summary
the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest
How To Make A Boxplot
– A central box is drawn from the first quartile (Q1) to the third quartile (Q3).
– A line in the box marks the median.
– Lines (called whiskers) extend from the box out to the smallest and largest observations that are not outliers.
– Outliers are marked with a special symbol such as an asterisk (*).
Standard deviation (calculation)
square root of the variance
standard deviation (definition)
measures the average distance of the observations from their mean. It is calculated by finding an average of the squared distances and then taking the square root.
Variance (calculation)
1) Square each deviation (observation-mean)
2) Find the “average” squared deviation. Calculate the sum of the squared deviations divided by (n-1)
Variance (defintion)
The average squared distance
Choose a measure of center and spread for a skewed distribution or a distribution with outliers
median and IQR
Choose a measure of center and spread for reasonably symmetric distributions that don’t have outliers
mean and standard deviation
bin/class width
X-scale
Are histograms quantitative or qualitative?
quantitative
Is mean or median more likely to be affected by extremes?
Mean
Is mean or median more resistant to change?
median
Modified boxplot
excludes outliers from whiskers
Population
Census
collects data from every individual in the population
Sample
a subset of the population in which we actually collect data
convenience sample
choosing individuals who are easiest to reach
Bias
A particular preference or point of view that is personal, rather than scientific.
voluntary response sample
people who choose themselves by responding to a general invitation
random sample

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