AP Stats - Unit 1

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

Simpson's Paradox

When averages are taken across different groups, they can appear to contradict the overall averages

histogram

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

stem & leaf or 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 distribution

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

symmetric distribution

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

left skewed distribution

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

right skewed distribution

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

first quartile

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

third quartile

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

Interquartile Range (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

advantage of stemplot

retains the actual data values from the data set

advantage of histogram

easy to see shape of distribution & good for large data sets

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

Describe the distributions

SOCS

Shape

Outliers

Center

Spread (Variability)

Variance equals

SD squared

Mean and SD are greatly affected by outliers, while median is resistant to changes- for symmetric distribution- use mean and SD, for skewed use outliers- use median and IQR

discrete variable

Consists of separate, indivisible categories. No values can exist between two neighboring categories.

continuous variable

a quantitative variable that has an infinite number of possible values that are not countable

Box plot

a graphic way of showing a summary of data using the median, quartiles, and extremes of the data

Median greater than mean

skewed left

Mean greater than median

data is skewed right