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A - Level Maths > Statistics > Flashcards

Statistics Flashcards

1
Q

What is a sample

A

Some subset of the population intended to represent the population

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2
Q

What is a sampling unit

A

Each individual in the population that can be sampled

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3
Q

What is a sampling frame

A

Numbered or named to form a list

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4
Q

Advantages of using a census

A

Should give completely accurate result.

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5
Q

Disadvantages of using a census

A

Time consuming and expensive.
Can not be used when testing involves destruction.
Large volume of data to process.

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6
Q

Advantages of using a sample

A

Cheaper
Quicker
Less data to process

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7
Q

Disadvantages of using a sample

A

Data may not be accurate.
Data may not be large enough to represent small sub-groups.

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8
Q

How to carry out simple random sampling

A

In sampling frame each item has identifying number. Use random number generator, or ‘lottery sampling’ (names in a hat

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9
Q

What is simple random sampling

A

Every sample has an equal chance of being selected

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10
Q

Advantages of simple random sampling

A

Avoids bias
Easy and cheap to implement
Each nu. Has an equal chance

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11
Q

Disadvantages of random sampling

A

Not suitable when population size is large
Sampling frame is needed

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12
Q

How to carry out systematic sampling

A

Elements chosen at regular intervals

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13
Q

Advantages of systematic sampling

A

Simple
Quick
Suitable for larger samples / populations

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14
Q

Disadvantages of systematic sampling

A

Sampling frame needed
Can introduce bias is sampling frame is not random

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15
Q

When is stratified sampling used

A

Used when sample is large + pop. Naturally divides into two groups

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16
Q

How to carry out stratified sampling

A

Population divided into groups (strata) and a simple random sample carried out in each group.

Same proportion (𝑠𝑎𝑚𝑝 𝑠𝑖𝑧𝑒 (𝑛))/(𝑝𝑜𝑝 𝑠𝑖𝑧𝑒 (𝑁) ) sampled from each strata.

Used when sample is large and population naturally divides into groups.

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17
Q

Advantages of stratified sampling

A

Reflect population structure

Guarantees proportion representation of groups within the population

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18
Q

Disadvantages of stratified sampling

A

Population must be clearly classified into distinct strata.
Selection within each stratum suffers from same disadvantages as simple random sampling.

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19
Q

How to carry out quota sampling

A

Population divided into groups according to characteristic. A quota of items/people in each group is set to try and reflect the group’s proportion in the whole population. Interviewer selects the actual sampling units.

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20
Q

Advantages of quota sampling

A

Allows small sample to still be representative of population.
No sampling frame required.
Quick, easy, inexpensive.
Allows for easy comparison between different groups in population

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21
Q

Disadvantages of quota sampling

A

Non-random sampling can introduce bias.
Population must be divided into groups, which can be costly or inaccurate.
Increasing scope of study increases number of groups, adding time/expense.
Non-responses are not recorded.

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22
Q

How to carry out opportunity sampling

A

Sample taken from people who are available at the time of study, and who meet the criteria

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23
Q

Advantages of opportunity sampling

A

East to carry out
Inexpensive

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24
Q

Disadvantages of opportunity sampling

A

Unlikely to provide a representative sample

High dependent on individual researcher

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25
Q

What is range
+ how to calculate e

A

It’s a measure of variation
Highest - lowest value

26
Q

What are percentiles

A

Divide data in 10
Eg.
Q1 = 25th percentile

27
Q

How to find a interpercentile range

A

Subtracted 2 percentiles

28
Q

How to find the mean

A

Total
——-
How many

Or

EX
—
n

29
Q

How to find mean from a table

A

Mid point x frequency
——————————
n

30
Q

What is the median

A

Middle data value when all the data values are placed in order of size

31
Q

What is the mode

A

Most frequently occurring data value

32
Q

Definition of an outlier

A

An observation that lies outside the overall pattern of distribution

33
Q

Give a reason to support the use of histograms to represent this data

A

……. Is continuous
Grouped

34
Q

What are the features of a histogram

A

No spaces between bars
Area is proportional to frequency

35
Q

frequency density equation

A

FD = F / CW

36
Q

What does area = on a histogram

A

Area = K x frequency

37
Q

Statistical distributions
What’s does X mean

A

A random variable
(It doesn’t have a fixed value)

38
Q

Statistical distributions
What does x mean

A

A particular value X can take

39
Q

What is a descrete random variable

A

Only have a certain number of possible values

40
Q

What do all probabilities add ot

A

1

41
Q

How do you tell which is the mode In terms of probability

A

the value with the biggest probability

42
Q

Statistical distributions
What is the binomial coefficient equation

A

(n) n n!
= C = ———-
(r) r r! (n-r)!

43
Q

Probability
What does n mean

A

2 shaped areas

44
Q

Probability
What does u mean

A

1 or 2 shaded areas

45
Q

What does mutant exclusive mean

A

No overlap

46
Q

What is the mutatly exclusive equation

A

P(AuB) = p(A) + p(B)

47
Q

What does independent eventsmean

A

No effect on each other

48
Q

Independent events equations

A

p(AnB) = P(A) x P(B)

49
Q

What is the formula of the regression line

A

Y = a + bx

50
Q

What is interpolation
Is it reliable

A

Values of x within the data range
It’s reliable

51
Q

What is extrapolation
Is it reliable

A

Use of values of x outside the data range
It’s unreliable

52
Q

What variable do you put on the xaxis

A

Independent

53
Q

What value do you put on the y axis

A

Dependent

54
Q

What is a hypothesis

A

A statement made about the value of a population parameter that we wish to test by collecting evidence in the form of a sample

55
Q

What is a null hypothesis

A

The default

56
Q

What is an alternative hypothesis

A

That there has been some change in the population parameter

57
Q

What is a test statistic

A

The evidence from the sample

58
Q

What is the level of significance

A

Is the maximum probability where we would reject the null hypothesis

59
Q

What is the critical region

A

The range of values f the test statistic that would lead to you rejecting H0

60
Q

What is the actual significance level

A

The actual probability of being in the critical region

A - Level Maths (4 decks)

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