Statistics

Question 1

Give the coding of x to get the standard normal distribustion

Answer 1

z = x - μ / δ

Question 2

Give the equation for friction

Answer 2

Fmax = μR

Question 3

Conditions for binomial distribution

Answer 3

Discrete
Fixed no. of trials
Success or failure
Trials independent
Constant probability of success

Question 4

Conditions for normal distribution

Answer 4

Continuous data
Symmetrical
Reduced frequency outside of mean

Question 5

Give the steps of binomial hypothesis testing

Answer 5

H0 - null hypothesis
H1 - alternative hypothesis
Define X
X ~ B(n,p)
Conclusion using significance level

Question 6

P(AnB) if independent

Answer 6

P(A)P(B)

Question 7

P(A|B) if independent

Answer 7

P(A)

Question 8

What is PMCC a measure of

Answer 8

Type and strength of correlation

Question 9

What % of data lies within 1δ of the mean on a normal distribution?

Answer 9

68%

Question 10

What % of data lies within 2δ of the mean on a normal distribution?

Answer 10

95%

Question 11

Give the 5 locations in the large data set in the UK from north to south

Answer 11

Leuchars
Leeming
Heathrow
Hurn
Cambourne

Question 12

Give the 3 international locations in the large data set and their countries

Answer 12

Beijing (China)
Perth (Australia)
Jacksonville (US)

Question 13

What are the two time periods in the large data set?

Answer 13

May - Oct 1987
May - Oct 2015

Question 14

What should be done with variables listed as ‘n/a’ or ‘-‘?

Answer 14

Ignored in calculations

Question 15

What should be done with variables listed as ‘tr’?

Answer 15

Use 0 or 0.025 as values, include in calculations

Question 16

Which locations in the large data set are close to the coast?

Answer 16

Jacksonville (US)
Perth (Australia)
Leuchars
Hurn
Cambourne

Question 17

Which location in the large data set is in the southern hemisphere?

Answer 17

Perth (Australia)

Question 18

What affects 1987 results in the UK?

Answer 18

Great storm 15-16 Oct
High wind speed in south and east

Question 19

Give all of the 9 variables in the large data set

Answer 19

Daily mean (air) temperature
Daily total rainfall
Daily total sunshine
Daily maximum relative humidity
Daily mean windspeed and direction
Daily maximum gust and direction
Cloud cover
Daily mean visibility
Daily mean pressure

Question 20

Give the units of daily mean (air) temperature

Answer 20

°C
1d.p.

Question 21

Give the units of daily total rainfall

Answer 21

mm
1d.p.
tr < 0.05mm

Question 22

Give the units of daily total sunshine

Answer 22

hr
1d.p.

Question 23

Give the units of daily maximum relative humidity

Answer 23

%
nearest integer
>95% mist and fog

Question 24

Give the units of daily mean wind speed and direction

Answer 24

kn (speed)
1kn = 1.15mph
degrees (direction)
nearest 10, cardinal direction

Question 25

Give the units of daily maximum gust and direction

Answer 25

kn (speed) 1kn = 1.15mph degrees (direction) nearest 10, cardinal direction

Question 26

Give the units of cloud cover

Answer 26

Oktas 0 1 2 3 4 5 6 7 8

Question 27

Give the units of daily mean visibility

Answer 27

dm 1dm = 10m horizontally

Question 28

Give the units of daily mean pressure

Answer 28

hPa (hectopascals) 1 hPa = 100 Pa = 1 milibar

Question 29

What is collecting data from an entire population called?

Answer 29

Census

Question 30

Give an advantage and disadvantage of a census

Answer 30

Fully accurate Time-consuming and expensive Can destroy all items if consumables e.g. fireworks

Question 31

What is collecting data from a population subset called?

Answer 31

Sampling

Question 32

Give advantages and disadvantages of sampling

Answer 32

Quicker and cheaper than census Less data to analyse than census Bias Incorrect population representation

Question 33

Define simple random sampling

Answer 33

Randomly selects n members of the population so that all members have an equal chance of selection by ordering them and selecting n random numbers (for sample size n)

Question 34

Define systematic sampling

Answer 34

Choose members of population at regular intervals from list e.g. every third house

Question 35

Define proportional stratified sampling

Answer 35

Population divided into groups (strata) e.g. by age then simple random sample from each stratum Proportion of sample from each stratum = proportion of population in that stratum

Question 36

Define quota sampling

Answer 36

Population split into groups, members selected until quota from that group is filled e.g. survey needing 25-30 females

Question 37

Define opportunity (convenience) sampling

Answer 37

Sample uses available population who fit criteria

Question 38

Give the formula for sample standard deviation of size n

Answer 38

Population standard deviation / sqrt(size of sample)

Question 39

Give the equation for the variance of a sample with size n

Answer 39

σ²/n Where σ is the original standard deviation ~N(μ,σ²/n)

Question 40

Define a sampling frame

Answer 40

A list of individuals in a population

Question 41

Give advantages and disadvantages of simple random sampling

Answer 41

No bias Easy and cheap to implement (for small populations) Each sampling unit has equal, known chance of selection Unsuitable if population or sample size is large Sampling frame (list) needed

Question 42

Give advantages and disadvantages of systematic sampling

Answer 42

Simple and quick to use Suitable for large samples and populations Can introduce bias if sampling frame isn't random Sampling frame (list) needed

Question 43

Give advantages and disadvantages of proportional stratified sampling

Answer 43

Accurately reflects population Guaranteed proportional representation Population must be split into strata Within strata - must have sampling frame, unsuitable for large population

Question 44

Define disproportional systematic sampling

Answer 44

Split population into strata Divide sample size by number of strata Choose that number of people from each stratum for surveying

Question 45

Give advantages and disadvantages of disproportional stratified sampling

Answer 45

Accurately represents population structure Split population into strata

Question 46

Give advantages and disadvantages of quota sampling

Answer 46

Small sample still representative No sampling frame needed Quick, cheap, easy Easy comparison between groups Non-random Must divide population into groups Increasing scope increases cost Nonresponses ignored

Question 47

Give advantages and disadvantages of opportunity sampling

Answer 47

Easy, cheap Not random Heavily biased Dependent on individual researcher Unlikely to be representative