UT OnRamps Statistics Midterm

data

facts / statistics collected together for reference / analysis

dataset

collection of data that can be analyzed as one unit

statistic

summarizes / analyzes data (ex: average)

variable

the characteristic being studied

numerical data

quantitative, consists of numbers

categorical data

consists of names, labels, or other nonnumerical values

discrete data

takes on only specific values, no decimal places

continuous data

can take on any value, can have decimal places

nominal data

categories with no specific order

ordinal data

categories with a specific order (5 star scale, sizes, etc)

population

collection of all possible members/outcomes for a group

parameter

calculation based on the whole population

sample

a subset of the population

statistic

calculation based on the sample

inference

using a sample statistic to estimate a population parameter

simple random sample (SRS)

choses x individuals from the whole population completely randomly

stratified random sample

separates the population into homogeneous groups (strata) and then choses a SRS from each group

convenience sample

choses individuals that are easiest to reach

sampling error

natural variation between sample estimation

bias

when we systematically over/under estimate a parameter because of the way the sample was collected

volunteer bias

when sample subjects are self selected

a bar graph is for __________ data

categorical

a histogram is for __________ data

numerical

bin width

width of an interval that is used in making a histogram.

left-skewed distribution

most of the data is on the right, mean > median

approximately normal

unimodal, symmetric, mean = median

right skewed distribution

most of the data is on the left, mean < median

multimodal distribution

Two or more peaks

uniform distribution

evenly spread out, no peaks

symbol for mean

x-bar (x̄)

standard deviation

average distance of points from the mean

five number summary consists of:

minimum, first quartile, median, third quartile, maximum

IQR (interquartile range)

Q3-Q1

what kind of plot shoes the five number summary

boxplot

measures of center and spread for approximately normal data

mean and standard deviation

measures of center and spread for skewed data

median and IQR

characteristics of a normal distribution

- perfectly symmetrical, unimodal, bell-shaped
- exactly half of the values are on the left, exactly half on the right
- mean = median = mode

68% of the data is within

1 standard deviation of the mean

95% of the data is within

2 standard deviations of the mean

99.7% of the data is within

3 standard deviations of the mean

standardized score is also known as a

Z-score

what is a z-score

number of standard deviations away from the mean

z-score formula

(x-mean)/standard deviation

sampling distribution

a probability distribution consisting of all possible values of a sample statistic

the mean of the sampling distribution is ___________ the mean of the population

equal to

variability of the sampling distribution__________ as sample size increases

decreases

standard deviation of all possible samples is the ___________

standard error

standard error formula

standard deviation/ square root of n

as sample size increases, the value of each sample mean is ____________ to the actual population mean

closer

normal approximation for the sampling distribution is used if _______ & __________

- the population is normally distributed
- sample size is greater than 30

acronym for describing a dataset

C - center
U - unusual features (outliars)
S - shape
S - spread