Edexcel Maths a level statistics

What are the two methods of simple random sampling?

• RNG (random number generator)

• Lottery sampling

How can we carry out a simple random sample?

You need a sampling frame (usually a list of the population). Each person is allocated a unique number and a selection of these numbers are selected at random

What is lottery sampling?

A method of simple random sampling. Members of the sampling frame are written down and drawn out of a hat to select participants randomly.

What is a simple random sample?

A sample where everyone has an equal chance of being selected.

What is a systematic sample?

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

How can we work out the interval for a systematic sample?

Divide population by sample size (eg, 100/20 is every 5th person in a population of 100 with a required sample size of 20)

What is stratified sampling?

The population is divided into mutually exclusive strata and a random sample is taken from each

What is the formula we can use to work out how many people we should take per strata?

Number sampled per strata = Population of strata/population x sample size required. It is a ratio

What are the advantages of a simple random sampling?

• Free of bias

• Easy and cheap to implement for small populations and sizes

• Each sampling unit has an equal chance of being picked

What are the disadvantages of a simple random sampling?

• Not suitable when population or sample size is large as it is time consuming, disruptive and expensive

• A sampling frame is needed

What are the advantages of systematic sampling?

• Simple and quick to use

• Suitable for large populations and samples

What are the disadvantages of systematic sampling?

• A sampling frame is needed

• Can introduce bias is sampling frame is not random

What are the advantages of stratified sampling?

• Sample accurately reflects the population structure

• Guarantees proportional representation of groups within a population

What are the disadvantages of stratified sampling?

• Population must be clearly classified into distinct strata

• Selection from each stratum have same disadvantages as simple random sampling

What are the types of random sampling?

• Simple random sampling

• Systematic sampling

• Stratified sampling

What are the types of non-random sampling?

• Quota sampling

• Opportunity sampling

What is quota sampling?

An interviewer or researcher selects a sample that reflects the characteristics of a whole population

How can we carry out a quota sample?

Population is divided into groups according to a characteristic. The size of each group determines the proportion of the sample selected from each group. each member of the population is assessed and assigned into a specific group. Once the quota has been filled , no more members are selected from that group.

What is another name for quota sampling?

Convenience sampling

What is opportunity sampling?

Consists of taking a sample from individuals who are available at the time of the study and fit the criteria you are looking for

What are the advantages of quota sampling?

• Allows a small sample to be representative of the population

• no sampling frame required

• Quick, easy and inexpensive

• Allows for easy comparison between groups

What are the disadvantages of quota sampling?

• Non-random sampling can introduce bias

• Population must be divided into groups which can be costly and inaccurate

• Increasing size of study can introduce more groups, which takes more time and is more expensive

• Non-responses are not recorded

What are the advantages of opportunity sampling?

• Easy to carry out

• Inexpensive

What are the disadvantages of opportunity sampling?

• Unlikely to provide a representative sample

• Highly dependent on individual researcher

What are quantitative variables/data?

Data/variables associated with numerical observations (numbers)

What are qualitative variables/data?

Variables/data associated with non-numerical observations (words)

What is a continuous variable?

A variable that can take any value within a given range

What is a discrete variable?

A variable that can take only specific values within a given range

What are the locations featured in the large data set?

• Perth

• Beijing

• Jacksonville

• Hurn

• Heathrow

• Leeming

• Leuchars

What is daily mean temperature and what are its units?

The average of the hourly temperature readings during a 24 hour period. Has units degrees celcius

What is daily total rainfall and what are its units?

Includes snow and hail which is melted to liquid water, measured over a 24 hour period. Has units millimeters. Amounts less than 0.05mm are recorded as trace

What is daily total sunshine and what are its units?

This is the sunshine recorded to the nearest tenth of an hour

What are daily mean wind directions units?

Given as bearings and as compass directions.

What is daily mean wind speed measured in?

measured in knots or from midnight to midnight. It is also measured using the Beaufort scale

What is the Beaufort scale?

A measure of how strong the wind speed is.

• 0 is calm (less than 1 knot)

• 1-3 is light (1 to 10 knots)

• 4 is modest (11 to 16 knots)

• 5 is fresh (17 to 21 knots)

What is daily maximum gust and what are its units?

Highest instantaneous windspeed recorded. The direction is also recorded. It is measured in knots.

What are daily maximum relative humidity’s units?

Given as a percentage of air saturation with water vapour.

What humiditi’s indicate fog or mist?

Above 95% relative humidity

What is daily mean cloud cover measured in?

Measures in oktas or eighths of the sky covered by clouds.

What is daily mean visibility and what is it measured in?

It is the greatest horizontal distance at which an object can be seen in daylight. It is measured in decametres

What is daily mean pressure measured in?

Hectopascals (hPa)

What is interpercentile range?

The difference between the values of two given percentiles

What are measures of location/measures of central tendencies?

Statistical values that summarize or represent the center or typical value of a dataset, such as mean, median, and mode.

What are measures of spread?

Statistical values that describe the dispersion or variability within a dataset, including range, variance, and standard deviation and interquartile range

What are mutually exclusive events?

When events have no outcomes in common

What are independent events?

When one event has no effect on the other event.

How can we work out whether something is independent?

P(A and B) = P(A)P(B)

How can we work out whether something is mutually exclusive?

P(A or B) = P(A) + P(B)