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Maths Equations > Stats > Flashcards

Stats Flashcards

1
Q

Definition of a population

A

A complete set of data where every element is included

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2
Q

Definition of a sample

A

A selection of the population

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3
Q

Definition of a census

A

Every element is surveyed. They are rare as it is expensive and labour intensive

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4
Q

Definition of a sampling frame

A

A list of sampling units (eg oktas for cloud coverage)

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5
Q

Random sampling methods

A

1) Simple random sample (eg random number generator or names out of a hat)
2) Systematic sample (eg all elements numbered. 1st element chosen random then every nth element is chosen eg pick random student 1-10 then every 10th student after this)
3) Stratified sample- proportions of groups in population represented in sample (eg if was 100 boys and 100 girls use 5 random boys and 5 random girls. if 103 boys, 107 girls use 9.8 boys (10) and 10.2 girls (10))

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6
Q

Non-random sampling methods

A

1) Opportunity sampling- whoever is present

2) Quota sampling- certain number from each group then filled first comes first served until quota filled.

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7
Q

Risk of non-random sampling

A

Risk of bias/ lack of equal representation

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8
Q

Qualative data

A

Non-numerical data eg colours, tv shows, etc

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9
Q

Quantative data

A

Numerical data eg height, number of siblings, etc

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10
Q

Discrete data

A

Type of quantative data.
Can only take certain numbers, usually whole numbers.
Few exceptions eg shoe sizes can have half sizes
Usually comes from counting

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11
Q

Continuous data

A

Type of quantative data.
Can take any decimal value in a certain range.
Usually comes from measuring

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12
Q

What is n/a replaced by in data

A

n/a is ignored

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13
Q

What is tr (trace) replaced by in data

A

0

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14
Q

Advantages of simple random samplings vs disadvantages

A

+ve:

1) Free of bias
2) Easy and cheap for small samples
3) Each sampling unit has a known and equal chance of selection

  • ve:
    1) Requires a sampling frame
    2) Unsuitable for larger samples/ populations as time consuming, disruptive and expensive
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15
Q

Advantages of systematic sampling vs disadvantages

A

+ve:

1) Simple and quick
2) suitable for larger samples/ populations

  • ve:
    1) Sampling frame required
    2) Can introduce bias if sampling frame is not random
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16
Q

Advantages of stratified sampling vs disadvantages

A

+ve:

1) Sample actively refelcts population structure
2) Guarantees representation of all groups within a sample/population

  • ve:
    1) Population must be clearly classifies into distinct groups
    2) Selcection within each stratum can be time consuming/ expensive and requires a sampling frame
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17
Q

Advantages of quota sampling vs disadvantages

A

+ve:

1) Allows even small samples to be representative of population
2) No sampling frame required
3) Quick, easy and inexpensive
4) Allows for easy comparison between groups in a population

  • ve:
    1) Non-random so can introduce bias
    2) Population must have seperate distincty groups
    3) Can be costly or inaccurate
    4) Non-responses are not recorded as such
    5) Increasing scope of stud/ number of groups adds time and expense
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18
Q

Advantages of opportunity sampling vs disadvantages

A

+ve:

1) Easy to carry out
2) Inexpensive

  • ve:
    1) Unlikely to provide representaive results
    2) Highly dependent on individual researcher
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19
Q

variance=

A

standard deviation^2

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20
Q

variance=

A

{fx^2/n - mean^2

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21
Q

How is standard deviation affected by coding

A

Affected by x and ÷, however not affected by + or -

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22
Q

How is mean affected by coding

A

Affected by both x and ÷, as well as + and -

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23
Q

Units for daily max temp

A

Degrees Celsius

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24
Q

Units for daily total rainfall

A

millimetres (mm). If the total amount of rainfall collected is less than 0.05 mm, it is referred to as a trace of rain

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25
Q

Units for daily total sunshine

A

given in hours and to one decimal place

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26
Q

Units for Daily Maximum Relative Humidity

A

Values for this are recorded as percentages (%). Relative humidities above 95% are associated with mist
and fog

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27
Q

Units for daily mean winspeed and daily max gust speed

A

The daily mean windspeed is given in knots. 1 knot is 1.15 mph. The windspeeds are also categorised according to the Beaufort scale

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28
Q

Units for Daily Mean Wind Direction and daily max gust direction

A

The value is given in degrees relative to the true north

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29
Q

Units for cloud cover

A

It is measured in eighths. The technical unit used in this case is called oktas.
0 oktas indicates a completely clear sky, while 8 oktas indicates complete overcast.

30
Q

Units for visibility

A

Metres (greatest horizontal distance at which an object can be seen)

31
Q

Units for pressure

A

hectopascals (hPa).

32
Q

Warmest/ highest temp places in large data set

A

Jacksonville (24.8)
Beijing (22.6)
As are in northern hemisphere so closest to equator

Not perth as is in Southern hemisphere

33
Q

Warmest locations in UK from large data set

A

Base on mean temperature: Heathrow (15.6), Hurn (14.1), Cambourne (13.6),

34
Q

Coldest location

A

Perth (15.2) outside UK

Leuchars (12.2) including UK

35
Q

Most rainfall

A

Based on mean rainfall:
Cambourne, UK - 2.8mm
Jacksonville, World wide -

36
Q

Dryest places

A

Heathrow, UK - 1.8mm

Heathrow, World wide - 1.8mm (If just B, J & P then Beijing at 2.1mm)

37
Q

Interpolation eqn

A

Lower bound + (how far through group/group frequency) x class width

38
Q

Histograms freqeuncy eqn

A 
Frequency= class width x frequency denisty
Area of each bar represents the frequency of the group
39
Q

When does a product moment correlation coefficient suggest there is a linear relationship between 2 variables

A

When is close to 1 (+ve linear) or close to -1 (-ve linear)

40
Q

P(AnB) for mutually exclusive events=

A

p(A) + p(B)

41
Q

Rules to check if 2 events are statistically independent (2 rules)

A

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

2) P(AlB) = P(a)

42
Q

n vs u meaning in probability

A 
P(XnY)= prob of x and y (intersection of x and y)
p(XuY)= prob of x or y
43
Q

How to find lower quartile for discrete data

A

n/4th data

If give a 0.5 number then round up to nearest whole observation

44
Q

Discrete uniform distribution meaning

A

When probability of each potential outcome is equal

45
Q

P(X=r) for x-b(n,p)

A

NCr x p^r x (1-p)^(n-r)

46
Q

P(A’)=

A

1- P(A)

47
Q

If mutual exclusive P(AuB)=

A

P(A) + P(B)

48
Q

P(AlB)=

A

P(AnB)/ P(B)

49
Q

Addition rule of P(AuB)

A

P(AuB)= P(A) + P(B) - P(AnB)

50
Q

Addition rule of P(AnB)

A

P(AnB) = P(A) + P(B) - P(AuB)

51
Q

Normal distribution eqn

A

X-N(mean, variance)

52
Q

Standard normal substitution for Z (used to find unknow values for mean/ standard distribution)

A

Z= (X- mean) / standard deviation

53
Q

Whicj=h may must inequality face for inverse normal distribution

A

< (same as binomial)

54
Q

Median of a normal distribution

A

for a normal distribution, mean = median = mode.

55
Q

What is the sign of the area for inverse normal on calc function

A

Uses prob less than observed value

56
Q

How many decimal places to use for Z values in normal dist question as this is how given in table of z values

A

give to 4dp

57
Q

How to tell if data has a +ve or -ve skew

A

+ve skew= mean> median

  • ve skew: meanQ2-Q1
  • ve skew Q2-Q1>Q3-Q2
58
Q

Formula for coefficient of skewness

A

Coefficient of skewness= 3(mean-median) / standard deviation

59
Q

What skew is required for a normal distribution

A

No skew/ slight skew/ almost symetrical distribution

60
Q

Sxx=

A

{x^2 - (({x)^2 / n ) = variance x n = in formula book

61
Q

Outlier eqns

A

Any value GREATER than: Q3 + k(Q3-Q1)
Any vlaue LOWER than: Q1 - k(Q3-Q1)
If K not given use k=1.5

62
Q

In question were says use log

A

use log_10 (use log button on calc)

63
Q

Q3=

A

3n/4

64
Q

Q1=

A

n/4

65
Q

y~ = y bar above =

A

mean of y

66
Q

Sx =

A

different version of st dev

67
Q

Sxx=

A

Variance /n

68
Q

standar dev =

A

square root of (Sxx/n)

69
Q

If y= ax^n for constants a and n then

A

y= log(a) + nlog(x)

70
Q

If y= kb^x for constants k and b then

A

log (y) = log (x) + xlog(b)

71
Q

Reasons to use a histogram

A

1) Continuous data

2) Unequal class widths

Maths Equations (16 decks)

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