Unit 1 - One Variable Data

variable

holds information about the same characteristic for many subjects

categorical variable

where the data collected places the individuals in various categories or groups, this data is best represented by a table

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

Relative Count

count/total

distribution

\- tells us what values the variable takes and how often it takes these values.

\- Describes how a quantitative variable behaves. Generally include shape, center, spread, & unusual features. (visualize)

bar graph

\- x axis has categorical variable

\- y axis has displays counts/percentages

\- each category has its own bars, do not touch

\- order in not important on x axis

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 plot

a display for quantitative data that uses place values to represent 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

\- MUST find out why it occurs

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

Discrete variables

are numerical values where counting makes sense, decimals would not be a good way to record the data

Continuous variables

are numerical values where decimals are appropriate; it usually involves some form of measuring

One-way Table

one variable

Bins

to make a histogram you have to put the data into bins which are even intervals that capture our data.

Bin Width

Stemplots

alternate way of illustrating data using a semi-graph, data is not lost (unlike histogram). Stem is first digit and leaf is second. needs a KEY

Back to back stemplots

created when you can separate the data into two categories. needs a KEY

Split Stem Leaf

when you have too many data values in a single stem, it can be helpful to split the stem; the same way we could create more bins on a histogram if our bin width resulted in a skyscraper

Dot plot

plotting data values with dots above corresponding values on a number line

Cumulative relative frequency graphs (ogives)

display percentiles

Percentile

will tell you what percent of data falls below a value

Factors of a Misleading Graph

\- putting a squiggle on the y axis, must start at a reasonable number

\- no labels on axes

\- different widths/volume on bars

\-

How to create an ogive

\- the first interval is 40-

If someone is at the 30th percentile what does that mean

less than 30% of the \[individuals\] were \[verb\] before the \[variable\] \[specific value\]

Describing Distributions

S: Shape

O: Outliers - typically visual on AP test

C: Center - mean/median, add context ex: symmetric

V: Variability - spread, standard of deviation

What is SOCV used to describe?

\- NOT USED to describe categorical variables

\- bc categories can be placed in any order on the x-axis, so shape would not make sense

\- same thing for center and spread, cannot find the avg zip code for ex.