Stat- Chapter 2 Descriptive Statistics

Mean

measure of center

adding all x values and dividing by the total n

Summation Symbol

adding terms

i=5 = 0+1+2+3+4+5=15

median

the middle value when the original data is arranged in increasing (or decreasing) order

mode

the most frequently occurring data value.

variance

measurement of dispersion across a data set

standard deviation

how much the values in a dataset vary from their mean

68% 95% 99%

Z-score

The -score converts a data value to a standardized scale

-= data is less then mean

+=data is greater then mean

unitless

Percentiles

divide the data into 100 groups of about 1% of the data in each group

p1, p2, p3.. p99

Quartiles

divide the data into 4 groups with about 25% of the data in each group

Q1,Q2,Q3

P25 = Q1 (lower quartile)

P50 = Q2 (median)

P75 = Q3 (upper quartile)

5 # summary

1)minimum

2) Q1

3)Q2

4)Q3

5)maximum

this can be used to make a boxplot

sample space

the set of all possible outcomes

ex. Rolling 1,2,3,4,5 or 6 dots with a single roll of a die.

event

a specific collection of such outcomes.

ex: Getting more than 3 dots when rolling a die.

Probability

that an event has occured or will occure

empirical probability

Empirical probability is the likelihood of an event estimated by dividing the number of times it occurs by the total number of trialsE

Complementary rule

the probability of an event not occurring is P(A′)=1−P(A)

union of 2 events

For any two events, if A or B or both occur, the probability is written as p(A or B) or the union of the events P(A u B) ano of the above

Intersection of 2 events

For any two events, if A and B occur, the probability is written as P(A and B) or the intersection of the events P(A n B)

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mutually exclusive

If the events A and B have no overlap they are disjoint, or mutually exclusive

Addition rule

P(A or B) = P(A) + P(B)

Conditional Probability

porbabiltiy of event B occuring given that A has already occured = P (B/A) and vise versa

Independent events

one event doesnt affect the probability of the other P(A) = P(B/A)

Multiplication or production rule

P(A AND B) = P(A) X P(B/A)

independent events : P(A and B) = P(A) x P(B)

Permutations

The number of arrangements when r items are selected, without replacement, from a set of n items

!

factorial symbol

Combinations

set collection of r items to be selected without replacement from a set of n items. Order or arrangement of the items does not matter

random variable

A random variable returns a single numerical value as an outcome of a specific random experiment. Random variables are classified as discrete or continuous. Example: the number of dots when rolling a single die.