Statistics AS Flashcards
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)
