stats - unit 1

statistics

the science of collecting, organize, summarizing, and analyzing information to draw conclusions or answer questions.

descriptive statistics

consist of organizing and summarizing data. It describes dad through the numerical summaries, tables, and graphs

population

an entire group to be studied

individual

person or object that is a member of the population being studied

sample

a group of individuals selected from the population

parameter

numerical summary of a population

statistic

a numerical summary of a sample

inferential statistics

uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result

census

a study in which the entire population is included in the sample

qualitative variable

classifications of individuals based on some attribute or characteristic.

EX) gender, hair color, etc

quantitative variable

provides numerical measure of individuals

EX) age, shoe size, etc

discrete variable

a quantitative variable whose possible values are separated by points on a number line

EX) points in a football game (WHOLE #)

continuous variables

quantitative variables that can take on any value in an interval on the number line

EX) weight, height (ANY NUMBER ON NUMBER LINE)

nominal measurement

level of measurement whose values name or categorize.

EX) days of the week, car color

ordinal measurement

level of measurement that values can be distinguished and ranked

EX) educational level, satisfaction level on a survey

interval measurement

level of measurement the differences of the values have meaning

EX) shoe size, temp

ratio measurement

level of measurement differences and ratios of the values have meaning

EX) # of siblings, # of fish in a lake

observational study

behavior of the individuals is simply observed

cross-sectional studies

collects information over a short period of time

case-control studies

uses past record to obtain information

cohort studies

observe a group of individuals over a long period of time

experiment

individuals are subjected to various treatments which can affect the results

treatment-group

in a study is a collections of individuals who receive a certain treatment

control group

a collection of individuals who DO NOT receive any treatment

lurking variable

a variable not considered in the study; can affect the value of the response variable

placebo

a fake drug/procedure administered to the control group

blind study

individuals who do not know whether or not they are in the treatment or control group

double-blind study

neither the individuals nor the person in touch with the individuals know who is in the treatment and control group

random assignment

process of assignment individuals from a sample to the treatment group and control group randomly

cofounding variable

a variable other than the explanatory variable that was considered in the study whose effect cannot be distinguished from a 2nd explanatory variable

explanatory variable

a variable that is used to explain or predict the outcome of a study

response variable

variable that is being measured and is dependent on another variable

simple random sample

of a size (n) is one that is chosen from a population in such a way that every possible sample of size n has an equally likely chance of being selected

frame

a list of all the individuals in the population

systematic sampling

selecting every _th person

steps for systematic sampling

1. find the size of frame, N

2. determine sample size, n

3. compute N/n and round down, this is k

4. randInt(1,k)

5. additional indiv are found by repeatedly adding k

stratified sampling

population is divided into subgroups (strata) and simple random sampling is preformed in each subgroup

steps for stratified sampling

1. divide the # of individuals by the # of individuals in the entire population and then multiply by the desired sample size. round to the nearest whole #

   1. use simple random sampling to choose the individuals from each subgroup

cluster sampling

population is divided into subgroups called clusters, then simple random sampling is uses to select some clusters

steps for cluster sampling

1. divide population into clusters and number them to form a frame

2. select a random sample of clusters

3. survey all individuals in each of the selected clusters

convenience sampling

data that is easy to collect without regard to randomness. voluntary response is most common

voluntary response

individuals choose to participate

sampling bias

favors one group of individuals

non-response bias

individuals who do not respond to the study have different views from those who did respond

response bias

surveyed people’s answers don’t agree with what they really thing. poorly worded questions can cause this

sampling error

error involved in using a sample to estimate info about a population

how to calculate relative frequency

frequency / sum of all frequencies

histrogram

bar graph where the width of the rectangle is the same the they touch each other

how to calculate class width

(max value - lower class limit) / # of classes

ROUND UP for the answer

how to find lower class limit

choose a number slightly less than the smallest value

how to calculate class midpoint

sum of lower class limits divided by 2

how to find cumulative freq

1. 1st cumulative freq value is the same as the 1st frequency value

2. add 1st cumulative freq value to the 2nd freq value and continue

how to find cumulative rel freq

cumulative freq / freq sum

mean

add all the values in the data set and divide by the number of observations

median

value that lies in the middle of the data when the data is arranged in ascending order

mode

# that is the most repeated in the data set

μ =

population mean

x̄=

sample mean

N=

number of values in the population

n =

number of values in the sample

formula to find the mean

sum of all values / N

formula to find the sample mean

sum of all values / n

mean is the best measure when the data

is approx symmetric m

median is the best measure when the data…

is skewed or when there is more than one extreme values

if data is skewed left

the mean is LESS than the median

if the data is skewed right

the mean is GREATER than the median

range =

largest value - smallest value

pie chart

circle divided into sectors

pareto charge

bar graph that are drawn in decreasing order or frequency

side by side bar graph

used to compare 2 data sets

deviation

difference between a data value and the mean

variance

mean of the squared deviations

standard deviation

square root of the variance

how to find standard deviation σ for POPULATION

σ = √(∑(xi - µ)² / N

how to find standard deviation (s) for SAMPLE

s = √(∑(xi - µ)² / (n - 1)

how to find variance for POPULATION

σ_²

how to find variance for SAMPLE

s²

resistance

little to no changes

sensitive

a lot of change

empirical rule

distribution bell shaped

68% - 1 SD

95% - 2 SD

99.7% - 3 SD

chebeshev’s rule formula

(1 - 1/k²) x 100%