Important Ideas from AP Statistics Unit 1

Define Quantitative Variable

Takes numerical values for a measured or counted quantity

Define Categorical Variable

Takes on values that are category names or group labels

Name the two types of variables (2)

1) Quantitative

2) Categorical

Br graphs show ____ (how many) or ______ (percent)

frequency; relative frequency

Formula for marginal %

B/C

Formula for joint %

A/C

Formula for conditional %

A/B

Describe Misleading Graphs (3)

1) Vertical axis must start at 0

2) Axes must have a scale

3) Beware of using images for bar graphs (called a pictograph)

Define Segmented Bar Graph

stack bars to make 100%

Define Mosaic Plot

Segmented bar graph where the width of the bars is proportional to the group size

Define Association (aka Correlation or Relationship)

If knowing the value of one variable helps us predict the other variable

When it says “Describe the distribution…” it means…

what data values you have and how they are spread out

When it says “Describe the distribution…” use…

CSOCS

What does CSOCS stand for?

C - Context

S - Shape

O - Outliers

C - Center

S - Spread

Describe C (first) from CSOCS

Context - what variable is being measured?

Describe S (first) from CSOCS

Shape - Right/left skew, symmetry, modes (peaks)

Describe O from CSOCS

Outliers - Unusual points (points far away from cluster)

Describe C (second) from CSOCS

Center - Mean, median, general center

Describe S (second) from CSOCS

Spread - Range (highest - lowest), IQR, standard deviation

True or False: Use the “-ly” words.

True

What are some “-ly” words? (3)

1) slightly

2) approximately

3) strongly

How to approximate median in a histogram?

1) Count frequencies to find total # of data values (sum)

2) Identify the median’s position in the data set (n+1)/2

3) Count frequencies (left to right) until you reach the median position (answer from 2)

4) Report the interval of possible values for the median

What is the method called when using a calculator?

Summary Statistics

What is the formula for standard deviation?

“Average” is also known as…

Typical

To interpret the standard deviation, use this sentence stem:

“The [context] typically vary/varies by [standard deviation] from [mean = x].”

Ex. The salaries at this company typically varies by $43,010 from the mean salary of $50,100.

Define Center

The median is resistant to skew and outliers. The mean is not resistant to skew and outliers, it follows it.

True or False: The mean is resistant to skew and outliers. The median is not resistant to skew and outliers, it follows it.

False

What does “… is resistant” mean?

not seriously affected by skew and outliers

Define Spread

The IQR is resistant to skew and outliers. The range and standard deviation are not resistant to skew and outliers.

True or False: The IQR is resistant to skew and outliers. The range and standard deviation are not resistant to skew and outliers.

True

What makes certain things resistant?

The position matters for them not the values

If the mean is to the right of the median, then it is _____ skewed; mean __ median

right; >

If mean and median are in the middle, then it is ____; mean ___ median

symmetric; =

If the mean is to the left of the median, then it is ____ skewed; mean ___ median

left; <

For symmetric distributions, use ____

mean

For skewed distributions or outliers, use ___

median

The median is the ____ point; ___% of the data is below it and ___% of the data is above it.

50; 50

The _____ quartile is the median of the lower half of the data. The ____ quartile is the median of the upper half of the data

first; third

The interquartile range (IQR) is defined as _____.

Q3 - Q1

An outlier is a data value that is way too ___ or way too ___.

small; big

Formula for Low Outliers:

any value < Q1 - 1.5(IQR)

Formula for High Outliers:

any value > Q3 + 1.5(IQR)

Whiskers only extend to the ______ and _____ value, not the ____.

smallest; largest; outliers

True or False: Whiskers do not always meet at the minimum and maximum.

True

Outliers can be determined… (2)

1) 1.5(IQR) method

2) Standard deviation method

Describe 1.5(IQR) Method (2)

• low outliers < Q1 - 1.5(IQR)

• high outliers > Q3 + 1.5(IQR)

Describe Standard Deviation Method (2)

• low outlier < mean - 2(Standard Deviation)

• high outlier > mean + 2(Standard Deviation)

Define Five Number Summary

A summary of a distribution of quantitative data consisting of the minimum, first quartile, median, third quartile, and maximum

What is the specific order of Five Number Summary?

minimum, Q1, median, Q3, maximum

Define Boxplots

A visual representation of the five number summary

When comparing distributions using CSOCS, use…

comparative language such as “less than”, “equal to”, or “more/greater than”