Sum of the data notation

Σx

Mean of the data notation

x bar

X bar =

Σx / n

Q1 =

n/4

Q2 =

n/2

n3 =

3n /4

IQR =

Q3 - Q1

X bar = (from frequency table)

Σx2 / Σf

Median from UNGROUPED data set

n + 1 / 2

Median from GROUPED data

n / 2

Linear interpolation =

x - lower bound / group width = percentile - lower bound / group width

σ^2 = (variance)

Σx^2/n - (Σx/n)^2

σ = (standard deviation)

Sqrt(Σx^2/n - (Σx/n)^2)

σ = (from coding)

Sqrt (Sxx summary stats / n)

σ^2 = (from frequency table)

Σxf ^2/Σf - (Σfx/Σf)^2

σ =(from frequency table)

Sqrt(Σxf ^2/Σf - (Σfx/Σf)^2)

Mean of y from code y = ax + b

a (x bar) + b

a times mean of x. Add b

Standard deviation of y from code y = ax + b

σy = a(σx)

a times standard deviation of x

Outlier definition

out of 1.5x IQR from Q1 or Q3

Or 2 standard deviations from mean

Frequency =

frequency density x class width x k

Where k is constant

Frequency = (from histogram)

k x area

Where k is a constant

How to draw a frequency polygon

Join up midpoints

Define cleaning the data

Removing incorrect data values (anomalies)

Define consistent

Smaller range/ standard deviation/ IQR

Define experiment

Repeatable activity that has a result that can be observed and recorded

Define outcome

A result from an experiment

Define sample space

A way to show all possible outcomes

Define event

An outcome/ outcomes

And

n

intersection

Or

u

Union

Not

A’

The complement of A

Define independent

Outcomes don’t affect each other

for independent events, P(A n B) =

P(A) x P(B)

For mutually exclusive, P(A n B) =

0

Define mutually exclusive

Events can’t occur together

For mutually exclusive, P(A u B) =

P(A) + P(B)

Universe

S, U, ξ

empty set

Φ

conditional probability

Probability of A given B has already occurred P(A|B)

P(A|B) =

P(A n B) / P(B)

for independent events, P(A|B) =

P(A)

because we know P(A n B) = P(A) x P(B) and P(B) / P(B) = 1

Two way table

Lists the frequencies for the outcomes of both events happening together (column and row)

find conditional probability from tree diagram

Second tree is P(B|A) , P(B’|A) and P(B|A’) and P(B’|A’)

So P(B) = P(B|A) + P(B|A’)

P(A u B) =

P(A) + P(B) x P(A n B)

discrete random variable

CAPITAL X or Y

P(X = x) meaning

Probability that random variable X takes value of x

Σ P(X = x) =

1

X is at most k

X =< k

X is no greater than k

X =< k

X is at least k

X => k

When can binomial distribution be used

Fixed number of TRIALS, n

fixed probability of success, p

OUTCOMES of each trial are independent

2 OUTCOMES only

mean of successful trials in binomial distribution

np

Variance of number of successful trials

np(1 - p)

let X =

NUMBER OF … (success outcome)

nCr =

n! / r! (n-r)!

P(X>a) = (for calculator)

1 - P(X<=a)

P(X>=a) = (for calculator)

1 - P(X<=a-1)

P(a < X < b) = (for calculator)

P(X <= b-1) - P(X <= a)

P(a =< X =< b) = (for calculator)

P(X <= b) - P(X <= a-1)