AP Stats Unit 1

Interpreting the Mean

The average value of insert quantitative variable is insert the value of the mean with units

Formula for Location of the Median

\frac{\left(n+1\right)}{2}

Interpreting the Median

The typical value of insert quantitative variable is insert the value of the median with units

Mode

The most common value, or peak of the data

Relationship between variance and standard deviation?

The standard deviation is the square root of the variance, and the variance is the squared version of the standard deviation

Sx

The standard deviation (of a sample)

\sigma

The standard deviation (of a population)

Interpreting the standard deviation

On average, each insert the context of the variable varies from the mean insert the context of the variable by insert the value of standard deviation with units

IQR (meaning and formula!)

The range of the middle 50% of the data (Q3-Q1)

Interpreting the IQR

The middle 50% of the data has a range of insert the value of the IQR with units

Five # Summary

Min, Q1, Med, Q3, Max

Outlier Rule (formulas)

Q1-1.5\cdot IQR=lowerfence & Q3+1.5\cdot IQR=upperfence as a note the mean plus or minus the standard deviation times two also works, but only when we are asked to use that formula specifically

Dotplots

Draw a horizontal axis and label it with a variable name. Scale the access from the minimum to the maximum value. Mark a dot above the location on the horizontal axis corresponding to each data value. Keep the spacing between the dots the same. Best used for quantitative sets of data.

The unusual occurrences (three)

Clusters, gaps, outliers

Range

Max-min (affected by extreme values, do not use with outliers)

If there are outliers or it is skewed use…

Median and IQR

If there are not outliers and it is not skewed…

Use mean and range

Percentage vs Proportion

Percentage = proportion times 100 (so the proportion is the decimal and the percent is the percentage)

Marginal distribution

The frequency of a singular variable. Ex. If there are 5 males in a study and 6 females the marginal distribution of gender is 45.45% male and 54.54% female

Conditional distribution

Looking at distributions within a category. Ex. If asked to find the conditional distribution of females you would take each data point and put it over the total for females, not the total for females and males

Discrete

Counting something (a fixed set of possible values with gaps between them)

Continuous

Measuring something (any value in an interval on a number line)