Stat 100 First Midterm

statistic definition

numerical measure calculated from sample

parameter definition

numerical measure calculated from whole population

difference in parameter and statistic?

parameter is calculated from the whole population, while the statistic is from a sample data set

the index value(i) means what

where in the data set we start from

n means what in sigma notation? (with the funky looking E)

end of the index

nth percentile means what?

n% of the sample lies below the value and 100-n% of the values lie above it

what does this equation give us? (P/100)(n+1)

index position number

T/F. to find percentiles we do not need to order data.

F, need to order data points

y tilde = what?

50th percentile

the 50th percentile is y tilde which is also known as the _____ or the ____ ____

median or the second quartile

the first quartile is also what percentile?

25th

third quartile is the ___ percentile

75th

mode is the…

most occurring value of y

can a data set have more than one mode?

yes

unimodal =

one mode

bimodal =

2 modes

trimodal =

3 modes

multimodal =

more than 3 modes

IQR is calculated how?

Q3 - Q1

what does the IQR give us?

the middle 50% of the data

sample variance is denoted by

s squared

sample variance is the what?

average squared distance from mean

T/F. We usually interpret sample variance.

F, it is in units squared so not usually interpreted

the denominator the fraction in the equation for sample variance is n-1, why?

to better estimated the population variance; removes bias

sd =

average distance from mean

relative frequency

frequency of event relative to total sample

relative frequency is usually in what numerical form?

decimal from 0 to 1

subject

thing that is what data is being measured on

variable

characteristic of subject that can be assigned number or category

random variable

variable whose outcome is result of random process

Do we know the outcome of a random variable in advance?

no

population

collection of all subjects of interest

sample

subset of population

n

sample size

simple random sample

sample where each subject has equally likely chance of being selected

a random variable, prior to being measured, is usually denoted how?

with a capital letter

observed values are denoted how?

lower case letter

in simple random sampling, the subjects are chosen…

independently of each other; choosing one does not change probability of choosing another

technical definition of srs

every sample of size n is equally likely as any other sample of size n

numeric random variables =

naturally measured as numbers

what are the two kinds of numeric random variables?

discrete and continuous

discrete random variable =

has specific number values

continuous random variable =

can take on any value

categorical random variable =

measured as groups/labels

what are the two kinds of categorical random variables?

nominal and ordinal

nominal random variable =

no natural order

ordinal random variable

has order

bar charts show…

frequency

if the scale of a bar chart is changed, say from percentage to relative frequency, is the interpretation of the graph changed?

no

stacked bar chart

data is grouped and stacked

stacked relative frequency plot

data is grouped, stacked, and on adds up to 100 percent

which is easier to interpret, stacked bar chart or stacked relative frequency?

stacked relative frequency since it is proportioned to all add up to 100

what is this?

side by side bar chart

histogram, data is shown how?

in intervals of equal width

since the values of data in a histogram are put into intervals, are there any gaps between them?

no

the intervals of data in a histogram can be graphed against what kinds of frequencies?

frequency, relative frequency, and percent

whiskers in a box plot show…

max and min values within fences

outliers are…

values outside fences

side by side box plots are good for…

comparing different groups

symmetric data can be seen visually when…

one half of data is the mirror of the other

left skewed data means that the…

left tail is longer

what is this skewed to?

left skewed

right skewed data means that..

the right tail is longer

what is this skewed to?

right skewed

normal dist. is usually seen visually as a…

symmetric bell shape

when a graph is right skewed, where are the mean, mode, median relative to each other?

mean is more towards the right where the outliers are. mode is the most left, since it is the most frequent value. median is the middle value, so it is between the mean and mode.

T/F. the mean of a dataset is NOT sensitive to outliers and will not be affected by them.

F, it is sensitive to outliers

is the mode affected by a skew in data?

yes, since it is the most frequent value, it will be affected by this

in a symmetric histogram, Q1, Q2, and Q3 are all _____ distanced from e/o.

equally

in a left skewed histogram, Q2 is closer to…

Q3

in a right skewed histogram, Q2 is closer to…

Q1

statistic = numerical measure of the…

sample

parameter = numerical measure of the…

population

y bar denotes the…

sample mean

s denotes the…

sample sd

p hat denotes the…

sample probability

p denotes the…

population probability

mu denotes the…

population mean

sigma denotes the…

population sd

experiment =

random process where outcome is not known

sample space

all possible outcomes of an experiment

event

a possible outcome

the theoretical probability assumes what two things?

that we know all possible outcomes and possible probabilities

empirical probability is also known as the ____ _____.

relative frequency

theoretical probability describes….

a population

empirical probability/relative frequency describes the probability within…

a sample

empirical probability is based on…

sample

law of large numbers

as sample size gets larger, the probability of event occurring in a sample approaches the theoretical probability of an event

sum of all probabilities for a situation should always equal

1

union of a and b is…

a occurs, b occurs, or both occur

intersection of a and b is…

a and b occur

disjoint/mutually exclusive means…

two events cannot occur at the same time

what is the notation for mutually exclusive?

p(A intersection B ) = 0(0 with cross through it)

independence means that the…

probability of one event does not affect prob of other event

If two events are mutually exclusive, does that mean that they are independent?

no

why, if two events are mutually exclusive, are they dependent?

if one event occurs, then the probability of B occurring within that same time is 0

sensitivity

probability of testing positive given that you have the condition

specificity

probability of testing negative given that you dont have the condition

False negative

individual with condition testing negative

false positive

individual without condition testing positive