Statistics unit 1

statistics

set of methods for obtaining, organizing, summarizing, presenting, and analyzing data.

data

characteristics measured on individuals or units

population

totality of individuals we want info

sample

subset of units in a population

variable

characteristics or property of an individual
ex: TIME until light bulb burns out
DISTANCE: traveled

categorical data

represent values of categorical variables, that places individuals into one of several group
ex: gender of newborn
eye colour

qualitative

relating to or involving comparisons based on qualities,
- categorical
- "types" names, symbol, things

categorical and ordinal

ordering makes sense for values of categorical variables

categorical and nominal

if the variables of ordering dont make sense

quantitative data

values quantitative variables for adding and averaging make sense
ex: height
exam scores
volume
sums

distribution of data

tells us what values a variable takes and how often it takes these values,
VALUES dont have to be quantitative

bar charts

display variables values on one axis and frequencies on the other,
- spaces imply no continuity
- categorical variables and displays categorical data.

bar and pie charts

categorical data

stemplots, histogram, timeplot

quantitative data

pie charts

visual representation of the relative frequency

minimum

the smallest possible quantity

maximum

the largest possible quantity

frequency distribution

count of how many of our data values fall into various predetermined classes or intervals

continuous variable

take any value within a given range
- type of quantitative
-ex: weight

discrete variable

- only take a countable number of values
ex: # of children in a family.
- measure in certains #'s
ex: number of pets

relative frequency or proportion

dividing the number of data values in each class by the total number of data values (sum)

proportion

values between 0-1,
- inclusive
- decimal representation of fractions
- proportion of intervals must add up to 1

histogram

- large amount of data
- form of a bar graph with no spaces
- reflect continuity

symmetric data

if histogram is its centre and divides it into approximate mirror image

time plots

used for plotting time series data,
- values measured over time
- time plotted on x-axis
- variable values plotted on y-axis
presented by points, connected to make a trend

measure of centre

-mode
-median
-mean

measure of spread

- range
- standard deviation

location and variability

are the two important features of a data set

mode

most frequently observed

median

middle of the set

mean

average

outliers

extreme values that dont affect the value of the MEDIAN
-"resistant" to the effect of outlier

mean, range, standard deviation

affected by outliers

median, mode

resistant by outlier

mean and median

symmetric distribution are equal

weighted mean

each of the data points contributing equally to the final average, some data points contribute more than others.

variability

the difference being exhibited by data points within a data set, as related to each other or as related to the mean

range

the difference between the highest and lowest values.

interquartile range

of a data set measures the length of an interval which covers the middle 50 percent of the ordered observations

percentiles

describes how a score compares to other scores from the same set.