AP Stats Exam Review

z-score formula

(x - mean) / SD

z-score meaning

number of standard deviations away from the mean

positive: above

negative: below

adding / subtracting a constant to each data point

shape: stays the same

center: shifts by however much we are adding / subtracting (mean & median)

spread: stays the same (range, iqr, sd)

multiplying / dividing data points by constants

shape: stays the same

center: multiplied by the constant (mean & median)

spread: multiplied by the constant (range, iqr, sd)

normal curve

1. symmetric/unimodal/bell-shaped

2. mean = median

3. most data points are near the center

simpson’s paradox

a trend that appears in different groups of data reverses when the groups are combined

CSOCS

Context, Shape, Outliers, Center, Spread

• use to describe data distributions

right skew

med < mean

left skew

med > mean

When do you use normalCDF?

When finding percentages from values

When do you use InvNorm?

When finding values from the percentages

normalCDF example problem

You take an IQ test and get a score of 124. Assume IQ scores are normally distributed with a mean of 100 points and a standard deviation of 15 points. What percentile are you at?

InvNorm example problem

What score would you have to earn on an IQ test to be below 88% of test-takers? Assume IQ scores are normally distributed with a mean of 100 points and a standard deviation of 15 points.

CDOFS

Context, Direction (±), Outliers, Form (linear/non-linear), Strength (strong/moderate/weak)

Correlation

measures the strength of a linear relationship

• r-values near -1 or 1 are strong

• r-values near 0 are weak

• no units

Residuals

distance between data points and LSRL

• positive: above LSRL

• negative: below LSRL

Interpreting Slope

For every 1 [unit] increase in [explanatory variable], our model predicts an average [increase/decrease] of [slope] in [response variable].

Interpreting y-intercept

When [explanatory variable] is zero units, our model predicts that the [response variable] would be [y-intercept].

Extrapolation

Using the model to predict outside the data range

Residual Formula

y-y^