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Maths/Further maths > Maths stats > Flashcards

Maths stats Flashcards

1
Q

What is a census

A

Measures or observes every member

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2
Q

What is a sample

A

Selection of observation taken from subset of pop used to find out about whole pop

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3
Q

Advantages of census

A

Results should be completely accurate

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4
Q

Disadvantages of census

A

Time consuming, expensive, cannot be used when testing destroys process and hard to process large quantity of data

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5
Q

Advantages of sample

A

Less time consuming and cheaper, fewer people have to respond, less data needs to be processed

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6
Q

What is random sampling

A

Each member of pop has equal chance of being selected

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7
Q

What is simple random sampling

A

Everything has equal chance of being selected

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8
Q

Advantages of simple random sampling

A

Free of bias, easy and cheap for small samples and pops and each sampling unit has known and equal chance of selectionDi

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9
Q

sadvantages of simple random sampling

A

Sampling frame needed and not suitable for large samples and populations

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10
Q

What is systematic sampling

A

The required elements are chosen at regular intervals from and ordered list

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11
Q

Advantages of systematic sampling

A

Simple and quick to use, suitable for large samples and large populations

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12
Q

Disadvantages of systematic sampling

A

A sampling frame is needed and bias introduced if sampling frame is needed, Bias introduced if sampling frame is not random

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13
Q

What is stratified sampling

A

The population is divided into mutually exclusive strata and a random sample is taken from each strata in proportion to size of strata

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14
Q

Equation for stratified sampling

A

(number in stratum x overall sample size) / number in population

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15
Q

Advantages of stratified sampling

A

Sample accurately reflects population structure, proportional representation of group within population

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16
Q

DIsadvantages of stratified sampling

A

Population must be clearly classified into distinct strata, same disadvantages as simple random within each strata

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17
Q

Two types of non random sampling

A

Quota sampling and opportunity sampling

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18
Q

What is quota sampling

A

An interviewer selects a sample that reflects the charecteristics of the whole opulation

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19
Q

Advantages of quote sampling

A

Allows small sample to still be representational of whole pop, so sampling frame, quick and cheap and easy comparison between different groups within a population

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20
Q

Disadvantages of quota sampling

A

Non random sampling can introduce bias, population must be divided into groups which can be costly or innacurate, increasing scope of study increases number of groups which adds time and money, non responses not recorded

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21
Q

What is opportunity sampling

A

Sample is taken from people who are available at the time and who fits criteriaA

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22
Q

Advantages of opportunity sampling

A

Easy and inexpensive

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23
Q

Disadvantages of opportuinity sampling

A

Unlikely to provide a representitative result and highly dependant on researches

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24
Q

Criteria for a binomial dist

A

The number of observations n is fixed.
Each observation is independent.
Each observation represents one of two outcomes (“success” or “failure”).

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25
Q

To make binomial suitable what would be ideal

A

LARGER N

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26
Q

Conditions for normal aproximation of binomial

A

Large n and p close to 0.5

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27
Q

State one disadvantage of using quota sampling compared with simple random
sampling.

A

nOT RANDOM SO CANNOT USE RELIABLY FOR INFERENCES

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28
Q

Mutually exclusive

A

Both cannot happen at once

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29
Q

P(A or B) mutulaly excluvive

A

P(A) + P(B)

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30
Q

Independent P(A GIVEN B )

A

P(A)

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31
Q

Reason to include outliers

A

It is a piece of data and we should include all pieces of data

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32
Q

Reasons to not include outliers

A

It is extreme and could unduly influence anaylsis or could be a mistake

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33
Q

Do you include NA at all when calculating mean

A

No

34
Q

State the assumption involved with using class midpoints to calculate an estimate of
a mean from a grouped frequency table.

A

Assumes values are uniformly distributed within the classes

35
Q

Why could random sampling not be used

A

It is not possible to have a sampling frame

36
Q

Conditions for normal dist

A

Variable has to be continuous

37
Q

P(x=5) for continuous

A

0 as continous

38
Q

+- standard deviation for normal

A

Point of inflection

39
Q

Numbers not in table

A

3sf

40
Q

Numbers in talbe

A

4 dp

41
Q

For normal mean=

A

Mode = median

42
Q

z=

A

x-mew / o

43
Q

Standard deviation binomial

A

np(1-p) root that

44
Q

Why would oyu have to times p vbalue by 2

A

For normal dist, it is ewual on both sides

45
Q

For cumalitive frequenct what value do you plot

A

Top value

46
Q

Histogram height

A

Work out area scale factor in relation to frequency (double check this )

47
Q

What is extrapolating

A

Estimate outside range (unreliable )

48
Q

What is interpolation

A

Estimate inside range

49
Q

What is the explanatory variables

A

The one thrat explains the other and that causes change

50
Q

What does close to 1 mean

A

Positive correlation

51
Q

Normal aprox

A

Make binomial and then make normal from that i think

52
Q

list

A

aDD 1/2 FOR MEDIAN

53
Q

Conditions for poisson aprox of binomial

A

Large n small p np <10

54
Q

variance of (3x-1)

A

square 3

55
Q

variance poisson

A

Mean or np(1-p)

56
Q

Conditions for poisson

A

Events must occur independently, events must occur singly, events cannot occur at same time, events occur at constant

57
Q

H0 for chi squared test

A

No difference between theoretical frequency and observed frequency

58
Q

Binomial need thing

A

Need to either succeed or fail

59
Q

What is area

A

Significance level

60
Q

DOR

A

(rows-1)(columns-1)

61
Q

EF

A

Row time column over grand

62
Q

What is needed for central limit theorum

A

Large sample size unless data is already normally distributed

63
Q

mean for nb

A

r/p

64
Q

variacne for nb

A

r(1-p)/p squared

65
Q

What is a type 1 erro

A

Actual significance error (chance they are lucky)

66
Q

What is type 2 error

A

Incorrectly accept h0 p(not critical region given h1 i true)

67
Q

What will reducing significane level (type 1 error) do

A

Increase type 2 error

68
Q

What does increasing n do to erorrs

A

Reduces type 2

69
Q

What is size

A

Type 1 errorh

70
Q

What is power

A

1-type 2 error

71
Q

size

A

Rejecting h0 given h0 is true

72
Q

Power

A

rejecting h0 given h1 is true

73
Q

variance

A

Dont divide by n if its a discrete uniform distribution

74
Q

If chi squared greater than critical value

A

Reject that it is a fitable modle

75
Q

g(1) always =

A

1

76
Q

Remember you can rearrange var formula for e(x)squared

A

ok

77
Q

What happens if proportion of defective things stays same and dof stays same but proportions can be ree allocated

A

No change in test statistic

78
Q

) Explain the relevance of the Central Limit Theorem in part (a)

A

CLT applies since the sample size is large B1 3.5b
CLT states that the sample mean/
S
is (approximately) normally
distributed

79
Q

formula for chi squared

A

(o-e)squared/E

80
Q

E in 2 wasy

A

Row total times column total / grand total

81
Q

Dof 2 way

A

(r-1)(c-1)

82
Q
A

Maths/Further maths (11 decks)

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