intro to statistics

frequency

number of values that fall within a given interval

interval

numerical width (ex. 50 ≤ x< 60)

modal class

class of values and intervals that appears most often

continuous variable:

has infinite possibilities in a range (ex. time)

difference between stratified and quantum sampling

The main difference is that in stratified sampling, you draw a random sample from each subgroup (probability sampling). In quota sampling you select a predetermined number or proportion of units, in a non-random manner (non-probability sampling

discrete variable:

only has particular values

mean

median

also the 50th percentile

mode

value with the highest frequency

cumulative frequency

when one value of the frequency is added to the sum of all the values that came before it

percentile

the score below which a certain percentage of the data lies. ex. if you score in the 95th percentile, that means 95% of other scored less than you

cumulative frequency graph

upper quartile:

75th percentile

lower quartile

25th percentile

interquartile range

Q3-Q1

spread/variation

how far the data ranges from the mean

range

the difference between the max and min values

box and whisker plot

upper boundary

upper quartile +(1.5)(IQR). any data larger than this is an outlier

lower boundary

lower quartile - (1.5)(IQR). any data smaller than this is an outlier

standard deviation σx

how consistent a set of values are

variance

standard deviation squared

finding σx on a calculator

stat→ edit → put the values in L1 (midpoint of each interval in L2 if using frequency) → stat → calc → 1. var stats (freq. list=L2 if using frequency) → calculate → enter

simple random sampling

everyone has an equal chance of being selected. ex. drawing names out of a hat

systematic sampling

selects members at regular intervals ex. polling every 20th customer. interval =population size / sample size

stratified sampling

sample has the same proportion from each stratum (group with commonality) as the population does, selected randomly

quota sampling

sample has the same proportion from each stratum (group with commonality) as the population does, selected specifically

cluster sampling

random selection from groups likely to be representative of the entire population instead of the whole population. ex. surveying employees from some Walmart stores instead of employees throughout the chain

multistage sampling

several levels of random sampling

voluntary sampling

members of a sample group are invited to participate

convenience sampling

members are chosen out of convenience

sampling bias

sample does not accurately represent population due to sampling technique/members chosen

non-response bias

groups are underrepresented because they chose not to respond

measurement bias

collection process affects the dependent variable. ex coercion, multiple choice survey

response bias

members give inaccurate answers

a sample has mean X and standard deviation O. if d is subtracted…

• mean = X-d

• standard deviation = O

• variance= O²

a sample has mean X and standard deviation O. if multiplied by p…

• mean =pX

• standard deviation =pO

• variance =p²O²

correlation

the relationship between 2 variable

correlation coefficient ( r )

measures the strength of correlation. ranges from -1 to 1

+r

positive correlation

-r

negative correlation

r=-1

perfect negative correlation

r=1

perfect positive correlation

r=0

no correlation

r is close to 1 or -1

strong positive/negative correlation

finding r on graphing calculator

stat→ x and y values in L1 and L2→ stat - calc→ 8 → calculate. make sure you switch diagnosticON by going into catalogue

line of best fit

A line that represents the trend or pattern in a scatter plot. It minimizes the distance between the data points and the line, showing the overall relationship between the variables. must pass through mean point

linear regression

method for finding line of best fit. Linear regression is used for predicting and understanding the impact of independent variables on the dependent variable. find by going to 4 instead of 8 (on graphing calculator)

x=my+c

the horizontal distance of points, found by switching the x and y columns

r2

closer to 1, the stronger the correlation