AP Stats U1

individuals

unique people, animals, or things in data set

variable

characteristic that changes from one individual to another

categorical variable

takes on values that the are category names or group labels

quantitative variable

takes on numerical values for a measured or counted quantity

categorical data

values of a categorical variable in a data set

quantitative data

values of a quantitative variable in a data set

Not all variables with # values are…

quantitative (ex: zip code)

frequency table

gives # of individuals(cases) in each category

A frequency table helps represent

distribution of categorical variable in tabular form

relative frequency table

gives proportion or % of individuals (cases) in each category

majority

more than 50%

Bar charts for categorial data

• Var name on horizontal axis; freq on vertical

• Scale axes (start at 0) + equal increments

• bars should be equal in width and LEAVE GAPS between them

Different sample sizes of 2 groups makes it hard to compare the distribution but comparison is easier if you calculate…

relative frequencies within each group in answer choices involve %s

What are the 2 types of quantitative variables?

• discrete variable

• continuous variable

discrete variable

can take on a countable # of values (with gaps, counted)

continuous variable

can take on infinitely many values, but they cannot be counted (no gaps, measured)

Histogram

• Use intervals of values and figure out how many #s you have in a certain interval and then graph it with a bar

• values of endpoints should be put into the var at the right side of them

• easier to make for larger data sets

How to describe a distribution of quantitative data?

• Shape

• Center

• Variability (Spread)

• Unusual features

Shape

• Symmetric: both sides are mirror images of each other

• Skewed left: the left side has a “tail”

• Skewed right: the right side has a “tail

• Unimodal: there is a singular peak

• Bimodal: there are two peaks

• Uniform: most values are the same

Unusual features

• Outliers

• Gaps + Clusters

first quartile (Q1)

the median of the 1st half of data set

third quartile (Q3)

the median of the 2nd half of data set

DO NOT include the median in the Q1 or Q3 set of values when trying to figure out the…

Q1 or Q3

Interquartile range

Q3-Q1

Standard deviation

typical distance that each value is away from the mean

Equation of SD!

Sum of all values minus the mean squared divided by the # of values - 1. Lastly sqr is taken of everything.

Square of SD is…

variance

Interpreting IQR

the middle 50% of the values for _____ has a range of ____(IQR)

Interpreting SD

the _______ from each sample typically varies by about ______ (SD) from the mean of _____ (Mean)

Position

Q1 and Q3

Method 1 for Outliers

Low Outlier < Q1 - 1.5IQR

High Outlier > Q3 + 1.5IQR

Method 2 for Outliers

Low Outlier < mean - 2SD

High Outlier > mean + 2SD

Non-resistant stats

Mean, SD, range are highly influenced by removing outliers

Resistant stats

Median and IQR are not greatly affected

For skewed distribution use…

median for center and IQR for variability

For symmetric distribution use…

mean for center and SD for variability

Five # summary

min, Q1, median, Q3, max

Skewed right

mean > median

Skewed left

mean < median

Symmetric

mean = median

Percentile

percent of data values less than or equal to a given value

Interpret

the value of _____ is at the pth percentile about (p)% of the values are less than or equal to _____

z-score (standardized score)

(data value - mean)/SD

Interpret z-score

the value of ______ is _______ (z-score) standard devs above/below the mean

Z-score and percentile can be calculated for distributions with…

any shape

z score positive =

value above mean

z score negative =

value below mean

Normal distribution

mound-shape (bell-curve) and symmetric

Many quantitative values can be modeled by a…

normal distribution

Normal distributions are determined by…

mean and SD

Empirical/68-95-99.7 Rule

the SDs of mean from 1-3 are 68%, 95%, and 99.7%

Area to left of Normal distribution

1. Take value at x and find z-score of it

2. Use z-score take to calculate probability

Area to right of Normal distribution

1- area to left of norm. dist.