AP Statistics: Unit 1 (Exploring One-Variable Data)

variable

a characteristic that changes from one individual to another

categorical variable

variable that takes on values that are category names or group labels

quanitative variable

variables that takes on numerical values for a measured or counted quantity

individuals

people, animals, or things described by a set of data

frequency table

A table used to show the number of times a variable occurs.

relative frequency table

a table used to show the proportions of variables

requirements for making categorical data bar charts

1.) label axis

2.) scale axis

3.) draw bars accurately

requirements for making categorical data pie charts

1.) include legend

discrete variable

variable that can take on a countable number of values (whole numbers)

continues variable

variable that can take on infinite values

advantages to a dot plot

shows every individual value in a data set; easy to see shape of the distribution

disadvantages to dot plot

difficult to make for large data sets

advantages to a stem and leaf plot

shows every individual values in a data set; easy to see shape of distribution

disadvantages to a stem and leaf plot

difficult to make for large data sets

how to describe distribution shape

symmetric, skewed left, skewed right, uniform, normal

symmetric distribution

right and left sides of histogram are approximately mirror images

skewed left distribution

data clusters to right with tail to left

skewed right distribution

data clusters to left with tail to right

uniform distribution

data is level

bimodal distribution

data creates two clusters

unimodal distribution

data creates one cluster

how to describe a distribution

shape, center, variability (spread), unusual features

what can be used to describe center of distibution

mean, median, quartile 1 and 3

mean

sum of all the data divided by the number of values

median

middle values of an ordered data set

quartile 1

the median of the lower half of the data

quartile 3

the median of the upper half of the data

what can be used to describe the variability of a distribution

range, interquartile range, standard deviation

range

the difference between the highest and lowest values in a distribution

interquartile range

The difference between the upper and lower quartiles.

standard deviation

typical distance that each value is away from the mean

standard deviation formula

sqrt { [(1)/(data size - 1)] [value - mean]^2 }

variance

standard deviation squared

variance formula

[(1)/(data size - 1)] [value - mean]^2

what letter represents data size

n

what letter represents the standard deviation

s

what symbol represents the standard deviaton

lowercase sigma

what symbol represents the mean

mu

what letter represents the mean

x bar

outlier

A value that "lies outside" most of the other values in a set of data.

IQR method to find outliers

an outlier is a value more than 1.5 x IQR below the first quartile or a value more than 1.5 x IQR above the third quartile

standard deviation method to find outliers

and outlier is a value located 2 or more standard deviations above or below the mean.

nonresistant summary statistics

summary statistics highly influenced by outliers (mean, standard deviation, and range)

resistant summary statistics

summary statistics not greatly influenced by outliers (median and IQR)

measures of center for a skewed distribution

median

measures of center for a symmetric distribution

mean

measures of variability for skewed distribution

IQR

measures of variability for symmetric distribution

standard deviation

5 number summary

minimum, Q1, median, Q3, maximum

advantages of a box plot

shows the five number summary and outliers; splits data into quartiles

disadvantages of a box plot

does not show every individual value; does not show shape of distribution

measure of center indications for skewed right distribution

mean is greater than median

measure of center indications for skewed left distribution

mean is less than median

measure of center indications for symmetric distribution

mean and median are approximately equal

percentile

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

standardized score (z - score) formula

(data value - mean)/(standard deviation)

what distribution shapes can percentiles and z score be applied to

any distribution shape

normal distribution

distribution that is mound shape ( or bell curve ) and symmetric

empirical rule

The rules gives the approximate % of observations within 1 standard deviation (68%), 2 standard deviations (95%) and 3 standard deviations (99.7%) of the mean

percent of data within one standard deviation of a normal distribution

68%

percent of data within two standard deviation of a normal distribution

95%

percent of data within three standard deviation of a normal distribution

99.7%

how to find percent of values to left of any x value (assumed normal distribution)

normalcdf (LB: -10^99; UB: X; Mu: mean; sigma: standard deviation)

how to find percent of values to right of any x value (assumed normal distribution)

normalcdf (LB: X ; UB: 10^99; Mu: mean; sigma: standard deviation)

how to find percent of values in between any x and y value (assumed normal distribution)

normalcdf (LB: X ; UB: Y ; Mu: mean; sigma: standard deviation)

how to find x value if given percent (assumed normal distribution)

inversenorm(area: percent of data to left of X; Mu: mean; sigma: standard deviation)