AP Statistics Unit 1 Test With Answers

objects described by a set of data

any characteristic of an individual

places an individual into one of several groups or categories

takes numerical values for which it makes sense to find an average

tells us what values a variable takes and how often it takes those values

describes two categorical variables, organizing counts according to a row variable and a column variable

the distribution of values of that variable among all individuals described by the table (for a two-way table)

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.

describes the values of that variable among individuals who have a specific value of another variable

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.

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.

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
Spread

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

the right and left sides of the graph are approximately mirror images of each other

the right side of the graph (containing the half of the observations with larger values) is much longer than the left side

the left side of the graph is much longer than the right side

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.

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.

the midpoint of a distribution

Q3 – Q1

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.

Call an observation an outlier if it falls more than 1.5 x IQR above the third quartile or below the first quartile

the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest

– 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 (*).

square root of the variance

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.

1) Square each deviation (observation-mean)
2) Find the “average” squared deviation. Calculate the sum of the squared deviations divided by (n-1)

The average squared distance

median and IQR

mean and standard deviation

X-scale

quantitative

Mean

median

excludes outliers from whiskers

the entire group of individuals about which we want information about

collects data from every individual in the population

a subset of the population in which we actually collect data

choosing individuals who are easiest to reach

A particular preference or point of view that is personal, rather than scientific.

people who choose themselves by responding to a general invitation