math s1

P(A)

P(B)

P(A’)

P(B’)

P(A’ intercept B)

P(A intercept B)

P(AUB’)

P(A’UB)

mutually exclusive events

events with no outcomes in common

mutually exclusive event set notations

P(A or B)

P(A or B) = P(AUB)

P(A) + P(B)

independent events set notations

P(A and B)

P(A and B) = P(A intercept B)

= P(A) x P(B)

P(W and X) / P(W intercept B)

is equa'l to

P(W) - P(W and not X)

P(WUX) formula with 1

= 1- P(neither W nor X)

P(WUX) formula with P(W intercept X)

= P(W) + P(X) - P(W intercept X)

P(A given B) formula

P(A intercept B) / P(B)

measures of spread

range

interquartile range

variance formula

standard deviation formula

variance grouped data formula

standard deviation grouped data formula

f.d =

frequency/class width

what is frequency represented by

area of histogram

what is a histogram used to store

continuous data

outlier

extreme value outside of overall pattern

outlier formula

any value greater than Q3 + k(Q3-Q1)

Q3 + k(IQR)

or less than Q1 - k(Q3-Q1)

Q1 - k(IQR)

how are data sets compared

• measure of location (mean, mode, median)

• measure of spread (IQR, standard deviation)

• can compare mean and standard deviation

• or median and iqr if extreme value

key thing to remember for stem and leaf diagrams

• draw a key

• always round up for positions

histogram area formula

area = k x frequency

area = wxh

how to know if something is positive skew

data mostly at lower values

mode<median<mean

Q2-Q1<Q3-Q2

how to know if something is negative skew

data mostly at higher values

mode>median>mean

Q2-Q1>Q3-Q2

how to know if something is symmetrical skew

data spread evenly

mode = median=mean

Q2-Q1=Q3-Q2

formula showing how skewed daa is

3(mean-median)/standard deviation

0 is symmetrical

• + is positive

• - is negative

mean formula

sum of x/n

combined mean formula

n1(mean of x1) + n2(mean of x2)/n1 + n2

given data revelas that 18 of the 25 in the frequency of a group were not in fact accurate, given that the values are below the median how owuld this effect the median

no change as values are all below median

given data revelas that 18 of the 25 in the frequency of a group were not in fact accurate, given that the values are below the median how would this effect the mean

decrease as f(x) will be lower

given data revelas that 18 of the 25 in the frequency of a group were not in fact accurate, given that the values are below the median how would this effect the standard deviation

increase as data becomes more spread out

data mostly at lower values

positive skew

mode<median<mean

positive skew

Q2-Q1<Q3-Q2

positive skew

data mostly at higher values

negative skew

mode>median>mean

negative skew

Q2-Q1>Q3-Q2

negative skew

linear regression equation

y = a + bx

b =

Sxy/Sxx

a =

mean of y - b(mean of x)

Sxy =

sum of xy - [(sum of x)(sum of y)]/n

Sxx

sum of x² - (sum of x)²/n

Syy

sum of y² - (sum of y)²/n

how to interpret pmc

value of r always falls between -1 and 1

Positive Correlation (r>0): As one variable increases, the other variable tends to increase.

Negative Correlation (r<0): As one variable increases, the other variable tends to decrease