Statistics AS

Question 1

Sum of the data notation

Answer 1

Σx

Question 2

Mean of the data notation

Answer 2

x bar

Question 3

X bar =

Answer 3

Σx / n

Question 4

Q1 =

Answer 4

n/4

Question 5

Q2 =

Answer 5

n/2

Question 6

n3 =

Answer 6

3n /4

Question 7

IQR =

Answer 7

Q3 - Q1

Question 8

X bar = (from frequency table)

Answer 8

Σx2 / Σf

Question 9

Median from UNGROUPED data set

Answer 9

n + 1 / 2

Question 10

Median from GROUPED data

Answer 10

n / 2

Question 11

Linear interpolation =

Answer 11

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

Question 12

σ^2 = (variance)

Answer 12

Σx^2/n - (Σx/n)^2

Question 13

σ = (standard deviation)

Answer 13

Sqrt(Σx^2/n - (Σx/n)^2)

Question 14

σ = (from coding)

Answer 14

Sqrt (Sxx summary stats / n)

Question 15

σ^2 = (from frequency table)

Answer 15

Σxf ^2/Σf - (Σfx/Σf)^2

Question 16

σ =(from frequency table)

Answer 16

Sqrt(Σxf ^2/Σf - (Σfx/Σf)^2)

Question 17

Mean of y from code y = ax + b

Answer 17

a (x bar) + b

a times mean of x. Add b

Question 18

Standard deviation of y from code y = ax + b

Answer 18

σy = a(σx)

a times standard deviation of x

Question 19

Outlier definition

Answer 19

out of 1.5x IQR from Q1 or Q3
Or 2 standard deviations from mean

Question 20

Frequency =

Answer 20

frequency density x class width x k

Where k is constant

Question 21

Frequency = (from histogram)

Answer 21

k x area

Where k is a constant

Question 22

How to draw a frequency polygon

Answer 22

Join up midpoints

Question 23

Define cleaning the data

Answer 23

Removing incorrect data values (anomalies)

Question 24

Define consistent

Answer 24

Smaller range/ standard deviation/ IQR

Question 25

Define experiment

Answer 25

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

Question 26

Define outcome

Answer 26

A result from an experiment

Question 27

Define sample space

Answer 27

A way to show all possible outcomes

Question 28

Define event

Answer 28

An outcome/ outcomes

Question 29

And

Answer 29

n
intersection

Question 30

Or

Answer 30

u
Union

Question 31

Not

Answer 31

A’
The complement of A

Question 32

Define independent

Answer 32

Outcomes don’t affect each other

Question 33

for independent events, P(A n B) =

Answer 33

P(A) x P(B)

Question 34

For mutually exclusive, P(A n B) =

Answer 34

0

Question 35

Define mutually exclusive

Answer 35

Events can’t occur together

Question 36

For mutually exclusive, P(A u B) =

Answer 36

P(A) + P(B)

Question 37

Universe

Answer 37

S, U, ξ

Question 38

empty set

Answer 38

Φ

Question 39

conditional probability

Answer 39

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

Question 40

P(A|B) =

Answer 40

P(A n B) / P(B)

Question 41

for independent events, P(A|B) =

Answer 41

P(A)

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

Question 42

Two way table

Answer 42

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

Question 43

find conditional probability from tree diagram

Answer 43

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’)

Question 44

P(A u B) =

Answer 44

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

Question 45

discrete random variable

Answer 45

CAPITAL X or Y

Question 46

P(X = x) meaning

Answer 46

Probability that random variable X takes value of x

Question 47

Σ P(X = x) =

Answer 47

1

Question 48

X is at most k

Answer 48

X =< k

Question 49

X is no greater than k

Answer 49

X =< k

Question 50

X is at least k

Answer 50

X => k

Question 51

When can binomial distribution be used

Answer 51

Fixed number of TRIALS, n
fixed probability of success, p
OUTCOMES of each trial are independent
2 OUTCOMES only

Question 52

mean of successful trials in binomial distribution

Answer 52

np

Question 53

Variance of number of successful trials

Answer 53

np(1 - p)

Question 54

let X =

Answer 54

NUMBER OF … (success outcome)

Question 55

nCr =

Answer 55

n! / r! (n-r)!

Question 56

P(X>a) = (for calculator)

Answer 56

1 - P(X<=a)

Question 57

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

Answer 57

1 - P(X<=a-1)

Question 58

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

Answer 58

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

Question 59

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

Answer 59

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