Unit 1 AP Statistics

Categorical variable

Variable that can be put into groups

Categorical variable displays

Bar graph, frequency table, two way table, pie chart, relative frequency table, mosaic plot

Quantitative variables

Variable measured numerically; discrete and continuous

Discrete quantitative variables

Finite, fixed

Continuous quantitative variables

Infinite

Quantitative variable displays

Dot plot, stem plot, histogram, box plot

Every value

Dot plots and stem plots show

Summary

Histograms and box plots show

Marginal relative frequency

Row or colum total/ table total

Joint relative frequency

Cell / table total

Conditional relative frequency

Cell / row or column total

Bar graph

Gap between data, order doesn't matter

Histogram

No gap in data, order matters, 5 number summary

Shape

Symmetric, skewed left, skewed right, or modal

Unusual features

Gaps, potential outliers

Center

Mean (symmetric), median (skewed)

Spread

Standard deviation (symmetric), range / IQR (skewed), variability

Skewed context

Distribution of [context] is [skew] with [outlier]. The center is [median].

Symmetric context

The [context] typically varies by [Sx] from the mean [x].

5 number summary

Minimum, Q1, median, Q3, maximum

Interquartile range

Q3 - Q1, width of the box

Skewed outliers

(Q1 - 1.5IQR), (Q3 + 1.5IQR)

Symmetric outliers

X +/- 2Sx

Resistant

Median and IQR

Non resistant

Mean, standard deviation, range

Symmetric

Mean ≈ median

Skewed left

mean < median

Skewed right

Mean > median

Frequency

How many

Relative frequency

Percent, # of a specific observation / total # of observations

Generalize

Only possible if random

Percentile

% Of data that is < or = to a specific value

Z-score shows

Relative position in a distribution

± a constant

Center will change, same shape

• / x/x a constant

Center will change, spread will change, same shape

68%

% Of data within 1SD of the mean

95%

% Of the data within 2SDs of the mean

99.7%

% Of data within 3SDs of the mean

Normcdf

Lower, upper, mean, standard deviation,

invNorm

Area, mean, standard deviation

Frequency

Count

Relative frequency

%

Cumulative relative frequency

Percentile

Z-score calculation

x - X / Sx

Approximately normal

Symmetric