STAT1450 Test 1

population

collection of all elements (people or things) of interest

example of population

ALL cscc students, ALL toddlers at daycare

sample

subset of the population actually surveyed- usually identified by the sample size (n=#)

example of sample

50 cscc students, 12 toddlers at daycare

parameter

summary values that comes from population data, usually noted by greek letters (mu=populaiton mean, sigma= population standard deviation)

statistic

summary values that come from sample data

descriptive statistics

facts/outcomes of collected data, describes what was collected (volleyball highlights)

inferential statistics

uses descriptive stats to make predictions or generalize the population (predictions for who will win the game)

data collection methods

census, simulation, experiment, sampling

census

collect “as is” data from the entire population (collect data from all stat1450 sp25 students)

simulation

collect “pretend” data- reduces times, risk and cost (flight simulation, study effects of meds on mice)

experiment

impose a treatment and record the response, often compares control (placebo) vs. experimental groups

sampling

collect “as is” data from a subset of the population (survey 30 randomly selected hair salon customers)

sampling methods

simple random, convenience, cluster, stratified, systematic

simple random

requires randomly selecting from a list of the entire population so that element of the population has the same change of being selected; this is the least biased sampling methods but the most costly/timely

example of simple random

drawing names from a hat, computer random dialing

convenience

survey those that are easily accessible, this is the most biased methods

example of convenience method

survey one class, phone in survey, magazine survey

cluster

sample all from a few pre-existing locations; in theory, each location is a good representation of the population (age, gender, etc)

example of cluster method

survey all students in 3 classes on campus

stratified

characteristic is determined that might bias the survey results (gender, politics, age) and sample equal/proportionate numbers from each

example of stratified method

20 male and 20 female, 100 democrat and 100 republican

systematic

sample every nth element of the population (every 3rd package on the assembly line)

qualitative data

words or numbers that describe words

examples of qualitative data

hometown, rank mood from 1-10, phone number, room number

quantitative data

number that represents counts or measurements

examples of quantitative data

age, gpa, number of siblings, “how much?”, total $

discrete data

finite number of outcome in any given interval, graph displays gaps

continuous data

infinite number of possible outcomes, graph displays no gaps/breaks

levels of measurement

nominal, ordinal, interval, ratio

nominal

“name”, qualitative data (words) that aren’t ranked, names something EX: hometown, zip code, favorite color

ordinal

“order”, qualitative data (words), that have an inherent rank, ranks words EX: military rank, class rank, letter grade

interval

quantitative data that has an arbitrary scale, zero does not mean absence of EX: clock time, temperature, year

ratio

quantitative data where zero means ‘nothing exists’, highest level of measurement EX: age, $, height, gpa

formula to find class width

(max-min)/ # of classes; round up to next whole #

histogram

• bar graph

• quantitative data

• bars touch

• horizontal axis: midpoints

• vertical axis: frequency

relative frequency histogram

• bar graph

• bars touch

• HA: midpoints

• VA: relative frequency

polygon

• line graph (connect dots)

• HA: midpoints

• VA: frequency

• goes up and down

ogive

• line graph

• HA: upper class limits

• VA: cumulative frequency

• always increases/ stays level

• NEVER decreases

stem and leaf plot rules

• numeric order

• can’t skip values

• at least 3 stems required

time series plot

• quantitative data

• show how something changes over time

• uses time units along HA (days, years, months)

• uses collected data along VA

dot plot

• quantitative data

• used to display shape

• stacked dots for data

box plot rule about outliers

there if an outlier if it is further than 1.5 from box

pareto chart

• qualitative data

• HA: categories

• gaps between bars

• go in decreasing height

• VA: frequency/ rel. frequency

• displays mode

• shape is data dependent

• common mode is brown hair color

pie chart

• qualitative data

• circle graph

• separate parts of a whole

• each section displays the amount

• all add to 100%

measures of center

mean, media, mode

mean

average, “not resistant measure”→ affected by extreme data

median

middle piece of data, considered “resistant measure”→ not affected by extreme data

mode

data that occurred most often, no mode if all values occurred the same number of times

trimmed mean

average caluclated from a “trimmed” data set, trime % of data from both low and high end of sorted list, then find mean of the remaining values

• Multiply % times n (sample number) to determine how many values to deleter from each end of the list

outliers

extreme values that pull the mean away from the center

best when no outliers exist

mean

best when outliers exist

median

measures of variation (spread)

range, standard deviation

range

max - min

standard deviation

average distance that each peice of data is away from the mean

• Sx= sample standard deviation

• Sigmax= population standard deviation

uniform distribution

no mode, mean=median

normal distribution

1 mode= mean= median (all in center top of peak)

skewed right

“positively skewed”, mean>median

skewed left

“negatively skewed”, mean<median

bimodal

2 modes, mean=median

empirical rule

only applies to normal distributions for k=1,2,3 respectively

empirical rule of 68%

mu (sample) ±1sigma (stdev sx)= 68%

empirical rule of 95%

mu ± 2sigma(stdev)= 95%

empirical rule of 99.7%

mu ± 3sigma=99.7%

chebyshev’s theorem

used when distribution is not normal, at least 1-(1/k²) of the data lie within k standard deviation of the mean

chebyshev’s theorem of 75%

mu (sample) ± 2(stdev)= 75%

chebyshev’s theorem of 89%

mu (sample) ± 3(stdev)= 89%

chebyshev’s theorem of 94%

mu (sample) ± 4(stdev)= 94%

coefficient of variation formula

stdev/mean; the smaller the CV- the more consistent the data

measures of relative position

percentiles, quartiles, z-scores, unusual data

percentiles

percent of data below a given value; P= #’s below given #/ total amount of #’s times 100

quartiles

divide data into quarters

• Q1: 25% of data is below this

• Q2: median, 50% of data is below this

• Q3: 75% of data is below this

z-scores

number of standard deviations a value is from the mean

• z= sample - mean/ stdev

• pos= above mean

• neg= below mean

• 0= exactly on the mean

unusual data

data that is more than 2 standard deviation from the mean, left or right