AP Statistics Chapters 1-3 and 12.2

variable

holds information about the same characteristic for many subjects

categorical variable

where the data collected places the individuals in various categories or groups

quantitative variable

where the data collected is numerical and it makes sense to use it for numerical operations

frequency table

lists the categories for a categorical variable and displays the counts for each category

relative frequency table

lists the categories for a categorical variable and displays the percenatges for each category

distribution

describes how a quantitative variable behaves. Generally include shape, center, spread, & unusual features.

bar chart

a display for categorical data that uses bar height to represent counts or percentages for each category

histogram

a display for quantitative data that uses adjacent bars to represent counts or percentages of values falling in each interval

stemplot

a display for quantitative data that uses place values to reprensent the distributions

dotplot

a display for either kind of data that uses a dot to represent each individual in the data set

measures of center

mean for distributions that are symmetric, median for all other distribution shapes

measures of spread

standard deviation for distributions that are symmetric, IQR for all other distribution shapes

uniform

a distribution whose shape is evenly distributed throughout the values it takes

symmetric

a distribution whose shape is unimodal and each side is roughly a mirror image of the other

left skewed

a distribution that has a concentration of data on the upper end and the tail on the left

right skewed

a distribution with a concentration of data on the lower end and the tail on the right

outliers

values that fall outside the overall pattern of the data

mean

the average of the data values

median

the value in the center of an ordered data set

range

the maximum data value minus the minimum data value

1st quartile

the value where 25 % of the data fall below it in an ordered list

3rd quartile

the value where 75% of the data falls below it in an ordered list

IQR

the third quartile minus the first quartile

percentile

the place in the data where a certain percentage of the data falls below that value

5 number summary

includes the minimum, first quartile, median, third quartile, & the maximum

modified boxplot

a display for quantitative data that graphs the five-number summary on an axis and shows outliers of they exist

variance

the standard deviation squared, it is a measure of spread

resistant

values that are not strongly affected by extreme values, the median is more resistant that the mean. The standard deviation is most strongly affected by extreme values

Conditional Distribution

Deals with the rows inside the table

Pie Graph

used to show parts of a whole

Segmented Bar Graph

used to compare the distribution of a categorical variable in each of several groups

Box and whisker plot

shows the variability of a data set using quartiles

Measure of center

Mean - Is not resistant to extreme values

Median - Is resistant to extreme values

Measures of Spread

Range - not resistant to extremes

Standard Deviation - Not resistant to extremes

IQR - Is resistant to extremes

SOCS

S - Shape

O - Outliers

C - Center

S - Spread

Standard Deviation

a computed measure of how much scores vary around the mean score

percentile

value with the same % of the observations at or less than it

cumulative relative frequency graph (ogive)

graph used to examine location with a distribution, grouping observations into equal width classes, shows accumulating % of observations as you move through the class in increasing order

z-score

a measure of how many standard deviations from the mean an observation falls, & in what direction

transformations

converting the original observations to another scale, can affect shape, center, & spread of a distribution

density curve

a curve that is always on or above the horizontal axis, & has area exactly 1 underneath it, describes the overall pattern of the distribution

mean of a density curve

the balance point which the curve would balance if made of solid material

median of a density curve

the equal-areas point which divides the area under the curve in half

µ

notation for the mean of a density curve

σ

notation for the standard deviation of a density curve

normal curve

symmetric, single-peaked, & bell-shaped

68-95-99.7 rule

in a normal distribution, 68% of values fall within 1σ of the mean, 95% fall within 2σ of the mean, & 99.7% fall within 3σ of the mean

standard normal distribution

has a mean of 0, & a standard deviation of 1

standard normal table (table A)

a table of areas under the standardized normal curve, the table entry for each z value is the area under the curve to the left of z

"C" normality plot

right skewed distribution

backwards "C" normality plot

left skewed distribution

linear normality plot

normal distribution

"S" normality plot

uniform distribution

explanatory variable

the one we think predicts change in the response (x)

response variable

measures an outcome of a study (y)

scatterplot

shows the relationship between two quantitative variables; one variable on the horizontal axis & the other on the vertical axis

direction, form, strength

characteristics used to look at the overall pattern of a scatterplot

outlier

striking departures from the pattern; an individual value that falls outside the overall pattern

positive association

when above average values of 1 tend to accompany above average values of the other

negative association

when above average values of 1 accompany below average values of the other

correlation

measures the strength of the linear relationship between two quantitative variables (r)

regression line

a line that describes how a response variable (y) changes as an explanatory variable (x) changes; used to predict the value of y for a given x

predicted value

value of response variable for a given value of x (y hat)

slope

the amount by which y is predicted change when x increases by 1 (b)

y-intercept

the predicted value of y when x = 0 (a)

extrapolation

the use of a regression line for predictions far outside the interval of values of explanatory variable (x) used to obtain the line; such predictions are often not accurate

least-squares regression line

line of best fit; makes the sum of the squared residuals as small as possible

residual

the difference between an observed y & the predicted y (y - y hat)

residual plot

a scatterplot of the residuals against the explanatory variable; help us assess whether a linear model is appropriate

standard deviation of the residuals

gives the approximate size of a typical prediction error (s)

coefficient of determination

the fraction of the variation in values of y that is accounted for by the LSRL of y on x (r-sq)

association vs causation

association does not imply causation; a strong association between two variables is not enough to draw conclusions about cause & effect; for causation, we need a well designed experiment

transforming data

performing simple transformations of the data using logarithms that can straighten a non-linear pattern

power model

y = ax^b where the variable is the base (to achieve linearity, take log of x & y)

exponential model

y = ab^x where the variable is the exponent (to achieve linearity, take log of only y)