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A-level Maths > stats AS > Flashcards

stats AS Flashcards

1
Q

sample

A

set of data values for a random variable

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2
Q

population

A

a group that you want to sample information about.

e.g. year 7 students in a school

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3
Q

sampling frame

A

a collection of the items available to be sampled

e.g. a list of all the year 7 students in a school

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4
Q

sample survey

A

when information is collected from a small representation of the population

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5
Q

sampling unit

A

the person/object to be sampled

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6
Q

sampling fraction

A

the proportion of available sampling units that are actually sampled

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7
Q

census

A

when all the population has information collected about them

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8
Q

simple random sampling

A

every item of the population has an equal chance of being picked

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9
Q

opportunity/convenience sampling

A

sampling whatever/whenever its easiest

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10
Q

stratified sampling

A

the population is divided into categories then a random sample is chosen from each category.
each categories size is proportional with the population.

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11
Q

cluster sampling

A

the population is divided into strata representative of the population. a random sample of clusters is chosen and every item in the chosen clusters is sampled.

a large number of small clusters is most accurate.

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12
Q

systematic sampling

A

every nth member is selected

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13
Q

quota sampling

A

the population is divided into groups and a given number from each group is sampled.

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14
Q

self-selecting sample

A

where people volunteer to taake part or are given a choice to participate.

may be bias as people may chose to express their opinions of certain matters.

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15
Q

unimodal

A

one bump

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16
Q

bimodal

A

two bumps

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17
Q

positively skewed

A

bump near beginning

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18
Q

negatively skewed

A

bump near end

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19
Q

median

A

n+1/2

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20
Q

frequency density

A

= frequency/ class width

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21
Q

discrete Variables

A

can only take certain values but not those in between

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22
Q

Bivariate data

A

two variables are assigned to each item

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23
Q

Mean =

A

(Σxf)/n

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24
Q

spearmans rank

A

shows association of the data

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25
Q

Pearsons Product Moment correlation Coefficiant

A

a measure of correlation, r

26
Q

standard deviation

A

σ = sqrt (( (Σx^2)/n)- μ^2)

27
Q

standard deviation with frequency

A

σ = sqrt (( (Σx^2f)/Σf)- μ^2)

28
Q

outlier

A

a point more than two standard deviations away from the mean

29
Q

varience

A

σ^2

30
Q

P(A∨B) =

for mutually exclusive events

A

P(A)+P(B)

31
Q

P(A∨B) =

for not mutually exclusive events

A

P(A) + P(B) - P(A∧B)

32
Q

Independent events

A

events that have no effect on each other

33
Q

prove events are not idependent

A

P(A∧B) =/= P(A) x P(B)

34
Q

P(B|A)

A

probability of event B given that event A has happened

35
Q

if an event if independent

A

P(B|A) = P(B|A’)

36
Q

P(A∧B) =

A

P(A) x P(B|A)

37
Q

how to run a simple random sample

A
  • give a number to each population member
  • Generate a list of random numbers
  • Match these numbers to the population members to select the samples
38
Q

simple random sample advantage

A

every member of the population has an equal

39
Q

simple random sample disadvantage

A

it can be inconvenient if the population is spread over a large area

40
Q

how is a systematic sample carried out

A
  • Give a number to each population member from a list of the full population
  • calculate a regular interval to use by dividing the population size by the sample size
  • generate a random starting point then follow the pattern
41
Q

systematic ample advantage

A

it can be used for quantity control on a production line. it should also give an unbiased sample.
it relatively easy.

42
Q

systematic ample disadvantage

A

The regular interval could coincide with a pattern, giving a biased/unrepresentative distribution.

43
Q

opportunity/convenience advantage

A

data can be gathered very quickly and easily

44
Q

opportunity/convenience disadvantage

A

it isn’t random and can’t be very biased

45
Q

Stratified sampling advantage

A

if the population can be divided up into distinct categories, its likely to give a representative sample.
different categories may differ and can be looked at independently.

46
Q

Stratified sampling disadvantage

A

its not useful when there aren’t any obvious categories

it can be expensive because of the extra detail involved

47
Q

Quota sampling advantage

A

it can be done when there isn’t a full list of the population.
The sampler continues to sample people until they have enough

48
Q

Quota sampling disadvantage

A

can be easily biased by the sampler

49
Q

Cluster sampling advantage

A

more practical

can incorporate other sampling techniques

50
Q

Cluster sampling disadvantage

A

less representative of the population

51
Q

tow-stage cluster sample

A

randomly choose the samples then randomly select people from each cluster

52
Q

Normal distrubution

A

X~N(μ, σ^2)

53
Q

σ

A

standard deviation

54
Q

σ^2

A

varience

55
Q

Standard normal distrubution

A

Z~N(0,1)

56
Q

standard normal distrubution formula

A

Z = (X-μ)/σ

57
Q

test for normal approximation to binomial

A

np>5

nq>5

58
Q

normal distrubution of a sample

A

~N(μ, σ^2/n)

59
Q

2/3 of normal distrubution

A

μ+-σ

60
Q

95% of normal distrubution

A

μ+-2σ

61
Q

99.7% of normal distrubution

A

μ+-3σ

62
Q

critical value for normal hypothesis test

A

μ+-k(σ/√n)

where k = Ф(significance level)

A-level Maths (6 decks)

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