Stats Flashcards by SAM FIFA

Definition of a population

A complete set of data where every element is included

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Definition of a sample

A selection of the population

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Definition of a census

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

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Definition of a sampling frame

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

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Random sampling methods

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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Non-random sampling methods

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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Risk of non-random sampling

Risk of bias/ lack of equal representation

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Qualative data

Non-numerical data eg colours, tv shows, etc

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Quantative data

Numerical data eg height, number of siblings, etc

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Discrete data

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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Continuous data

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

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What is n/a replaced by in data

n/a is ignored

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What is tr (trace) replaced by in data

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Advantages of simple random samplings vs disadvantages

+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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Advantages of systematic sampling vs disadvantages

+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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Advantages of stratified sampling vs disadvantages

+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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Advantages of quota sampling vs disadvantages

+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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Advantages of opportunity sampling vs disadvantages

+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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variance=

standard deviation^2

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variance=

{fx^2/n - mean^2

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How is standard deviation affected by coding

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

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How is mean affected by coding

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

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Units for daily max temp

Degrees Celsius

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Units for daily total rainfall

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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Units for daily total sunshine

given in hours and to one decimal place

Units for Daily Maximum Relative Humidity

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

Units for daily mean winspeed and daily max gust speed

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

Units for Daily Mean Wind Direction and daily max gust direction

The value is given in degrees relative to the true north

Units for cloud cover

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.

Units for visibility

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

Units for pressure

hectopascals (hPa).

Warmest/ highest temp places in large data set

Jacksonville (24.8) Beijing (22.6) As are in northern hemisphere so closest to equator Not perth as is in Southern hemisphere

Warmest locations in UK from large data set

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

Coldest location

Perth (15.2) outside UK | Leuchars (12.2) including UK

Most rainfall

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

Dryest places

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

Interpolation eqn

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

Histograms freqeuncy eqn

``` Frequency= class width x frequency denisty Area of each bar represents the frequency of the group ```

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

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

P(AnB) for mutually exclusive events=

p(A) + p(B)

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

1) P(AnB) = P(A) x P(B) | 2) P(AlB) = P(a)

n vs u meaning in probability

``` P(XnY)= prob of x and y (intersection of x and y) p(XuY)= prob of x or y ```

How to find lower quartile for discrete data

n/4th data | If give a 0.5 number then round up to nearest whole observation

Discrete uniform distribution meaning

When probability of each potential outcome is equal

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

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

P(A')=

1- P(A)

If mutual exclusive P(AuB)=

P(A) + P(B)

P(AlB)=

P(AnB)/ P(B)

Addition rule of P(AuB)

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

Addition rule of P(AnB)

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

Normal distribution eqn

X-N(mean, variance)

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

Z= (X- mean) / standard deviation

Whicj=h may must inequality face for inverse normal distribution

< (same as binomial)

Median of a normal distribution

for a normal distribution, mean = median = mode.

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

Uses prob less than observed value

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

give to 4dp

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

+ve skew= mean> median - ve skew: meanQ2-Q1 - ve skew Q2-Q1>Q3-Q2

Formula for coefficient of skewness

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

What skew is required for a normal distribution

No skew/ slight skew/ almost symetrical distribution

Sxx=

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

Outlier eqns

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

In question were says use log

use log_10 (use log button on calc)

Q3=

3n/4

Q1=

n/4

y~ = y bar above =

mean of y

Sx =

different version of st dev

Sxx=

Variance /n

standar dev =

square root of (Sxx/n)

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

y= log(a) + nlog(x)

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

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

Reasons to use a histogram

1) Continuous data | 2) Unequal class widths