Data collection (+ Large Data Set facts)

What is a population?

The entire set of items (sampling units) that are of interest

What is a census?

An observation or measurement from every member of a population

What are the advantages and disadvantages of taking a census?

ADV: Should give a completely accurate result.
DISADV: 1. Time consuming for large populations, 2. expensive for large populations, 3. cannot be used when the testing process destroys the item (e.g. testing the battery life), 4. difficult to process large quantity of data

What is a sample?

A selection of observations or measurements from a subset of the members of a population

What are the advantages and disadvantages of using a sample?

ADV: 1. Less time-consuming than a census, 2. Cheaper than a census 3. Easier to process all of the data 4. Practical for tests where the items are destroyed
DISADV: 1. Doesn't measure every member of the population — inaccurate and not fully representative, 2. Sample size might not be large enough to represent the entire population

What does the size of a sample depend on?

The required accuracy and available resources

Generally, what creates a more accurate sample?

The larger the sample, the more accurate it is but you will need greater resources

If the population is varied, what do you need?

You need a larger sample than if the population were uniform

What can different samples lead to?

Different conclusions due to the natural variation in a population

What can the size of a sample affect?

The validity of any conclusions drawn

What is a sampling unit?

Individual units of a population (e.g. one single avocado)

What is a sampling frame?

A named or numbered list of each sampling unit in a given population

What does random sampling help to remove?

Bias

What are the three methods of random sampling?

1. Simple random sampling
2. Systematic sampling
3. Stratified sampling

What is a simple random sample and how is one taken?

Items from the sampling frame are selected at random, so each sampling unit has an equal chance of being selected. A random number generator is used alongside a sampling frame.

What is a simple random sample of size n?

One where every sample of size n has an equal chance of being selected

What are the advantages (2) and disadvantages(3) of simple random sampling?

ADV: 1. Bias free, 2. Simple and easy to do
DISADV: 1. Sampling frame required, 2. Time-consuming for large samples, 3. Doesn't accurately represent the proportions of the population

What is systematic sampling and how is it carried out?

All items of the sampling frame are ordered, and the items in this ordered list are selected at regular intervals. (Every kth unit is chosen, a random number between 1 and k is the starting point).

What are the advantages (2) and disadvantages (2) of systematic sampling?

ADV: 1. If sampling frame is randomly ordered, there should be no bias, 2. Quick to use, 3. Suitable for large sample sizes
DISADV: 1. Sampling frame required, 2. Non-randomly ordered data may introduce bias

What is stratified sampling?

• The population is first divided into mutually exclusive strata (groups/categories) and the number of members in each category is noted.
• The sample is then made up of a proportionally representative number of members to reflect the population.

What are the advantages (3) and disadvantages (2) of stratified sampling?

ADV: 1. Represents population structure, 2. Guarantees representation of all groups in population, 3. Can observe relationships between subgroups
DISADV: 1. Sampling frame needed, 2. Need clear strata/categories/groups in the population, 3. Time-consuming to split a large population into categories

How do you calculate the number sampled in a stratum?

(Number in stratum/number in population) x overall sample size

What are two methods of selecting numbers for random sampling?

1. Generating random numbers using a calculator, computer or random number table.
2. Lottery sampling

What happens in lottery sampling?

The members of the sampling frame could be written on tickets and placed into a 'hat'. The required number of tickets would then be randomly pulled out

What are two types of non-random sampling? What is their advantage?

1. Quota sampling
2. Opportunity sampling
   No sampling frame required

What is quota sampling?

1. Researcher splits population into groups, and the approximate size of each group is noted
2. A quota to be filled is noted down for each group (this may or may not be representative of the population).
3. The quotas are then filled using opportunity sampling. If any member is selected for a quota that has already been filled, they are ignored and move on.

What are the advantages and disadvantages of quota sampling?

ADV: 1. No sampling frame needed, 2. Allows a small sample to still be representative of the population, 3. Easy, cheap
DISADV: 1. Non-random sampling can introduce bias, 2. Population must be divided into groups which can be difficult or costly or inaccurate, 3. Not possible to find sampling errors

How do you determine a suitable quota?

• use electoral register to determine the size of each group as a proportion of the whole population
• assign the quotas as the same proportion of the whole sample

What is opportunity sampling?

Consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for

What are the advantages and disadvantages of opportunity sampling?

ADV: 1. Easy and cheap to carry out, 2. No sampling frame needed
DISADV: 1. Unlikely to provide a representative sample

2. Results can vary depending on the individual researcher

What are quantitative variables/data?

Numerical data

What are qualitative variables/data?

Non-numerical data

What is a continuous variable?

A variable that can take any value in a given range

What is a discrete variable?

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

What do class boundaries tell you?

The maximum and minimum values that belong in each class

What does the midpoint tell you?

The average of the class boundaries

What does the class width tell you?

The difference between the upper and lower class boundaries

What is the large data set?

Weather data samples provided by the Met Office for 5 U.K. weather stations and 3 overseas, over 2 set periods of time : May to October 1987 and 2015. These are: Leuchars, Leeming, Heathrow, Hurn, Camborne, Jacksonville, Perth and Beijing

What is the daily mean temperature?

The average of the hourly temperature readings during a 24 hour period

What is the daily total rainfall?

including solid precipitation such as snow and hail, which is melted before being included in any measurements - amounts less than 0.05 mm are recorded as 'tr' or 'trace'

What is daily total sunshine?

Recorded to the nearest tenth of an hour

What is daily mean wind direction and wind speed?

In knots, averaged over 24 hours from midnight to midnight. Mean wind directions are given as bearings and as cardinal directions. The data fro mean windspeed is also categorised according to the Beaufort scale

What is daily maximum gust?

The highest instantaneous windspeed recorded - measure in knots

What is daily maximum relative humidity?

Percentage of air saturation with water vapours. A continuous variable that can take any value within 0-100.

What is daily mean cloud cover?

Measured in oktas or eighths of the sky covered by cloud. Cannot be higher than 8.

What is daily mean visibility?

Measured in decametres (Dm). This is the greatest horizontal distance at which an object can be seen in daylight

what is daily mean pressure?

Measured in hectopascals (hPa)

Give all 8 locations used in the LDS and information about them

UK

• Leuchars - northernmost weather station, on the coast

• Leeming - in the north

• Camborne - On the coast, in the south (to the west)

• Heathrow - in the south

• Hurn - In the south, on the coast

International

• Jacksonville, USA

• Beijing, China

• Perth, Australia - the only weather station in the southern hemisphere

In which two years was the data in the LDS recorded, and between which months?

• 1987 and 2015

• Between May (1st May) and October (31st October)

• It measures one spring month, three summer months (June, July, August) and autumn months

Which measurements (4) were taken in the international locations?

• daily mean temperature

• Daily total rainfall

• Daily mean pressure

• Daily mean wind speed

Which measurements (11) were taken in the international locations?

• daily mean temperature

• Daily total rainfall

• Daily mean pressure

• Daily mean wind speed

• daily mean wind direction

• Daily maximum gust

• Daily max gust direction

• Daily total sunshine

• Daily maximum relative humidity

• Daily mean total clouds

• Daily mean visibility

Daily mean temperature. How is it measured, what are the units, and what is the range? What are the trends for international locations (3)?

• Measurement: every hour of a day they measure the temperature, find mean at the end

• Units: Celsius (1 dp)

• Range: 4-33 degrees Celsius

• Trends: Beijing and Jacksonville are hot locations. Beijing has a wide range of temperatures. Perth isn’t hot (seasons are flipped).

Daily total rainfall. How is it measured, what are the units, and what is the range? What are the trends for UK (1) and international locations (3)?

• Measure rainfall in a measuring cylinder over the day (includes all precipitation like snow and sleet)

• units: millimetres (mm), 1dp

• Range: 0-60 mm.

• tr values = trace. Trace means rainfall was less than 0.05 mm. In exams, you can say that tr is any value in [0, 0.05] or simply use 0.

• UK trends: wetter in the north

• Intl trends: Perth is wet as seasons are flipped. It has some days with really heavy rainfall (102 mm, 104 mm). Jacksonville is wet.

Daily mean wind speed. How is it measured, what are the units, and what is the range? What are the seasonal trends (2), trends for the UK (1) and international locations (3)?

• Measurement: record wind speed throughout the day, find mean at the end

• Units: knots (kn)

• Range: 3-19 kn

• Some N/A values, probably equipment error. Can ignore these values

• Seasonal trends: less windy in summer, windiest in autumn

• UK trends: coastal towns typically windier

• Intl trends: Beijing, Jacksonville not that windy. Perth

Daily max gust (UK only). Measurement, units, range, trends?

• Find max wind speed in a day

• Units: knots (kn), rounded to integer

• Range: 8-52kn

• Same trends as daily mean wind speed

Daily mean wind speed direction (UK only). Units and range?

• The direction the daily mean windspeed is coming from

• Two possible units given: an angle, given as a bearing to the nearest 10 degrees (range is 0-360 degrees), or cardinal point (compass point abbreviated to N, NE, SE, etc)

Daily max gust direction (UK only). Measurement?

• the direction that the daily max gust is coming from

• Mean windspeed direction and max gust direction tend to be the same

Daily mean pressure (all locations). Measurement, units and range?

• record pressure throughout the day, find mean at the end

• Units: Hectopascal (hPa), rounded to integer

• Range: 988 - 1038 hPa

Total sunshine (UK only). Measurement, units, range, seasonal trends, UK trends?

• how many hours of sunshine there were in a day

• Units: hours, rounded to 1 dp

• Range: 0 - 14 hours

• Seasonal trends: more sunshine in the summer

• UK trends: less sunshine in the north

Daily max relative humidity (UK only). Measurement, units, range, other key facts?

• Max humidity recorded in the day

• Units: %, rounded to integer

• Range: 80% - 100%

• If humidity > 95%, gives rise to mist and fog

Daily max total clouds (UK only). Measurement, units, range?

• divide sky into 8 sections. Number of sections with clouds = number of oktas.

• Units: oktas, only integer values

• Range: 0 - 8 oktas

Daily mean visibility (UK only). Measurement, units, range?

• furthest distance they can see an object

• Units: Dm (1 Dm = 10m), rounded to nearest 100 Dm

• Range: 200-5000 Dm (but some values lie outside this range)

Why might a median be less than a mean?

• the distribution is skewed
• a few large distances distort the mean

Why would you use the median and interquartile range rather than the mean and standard deviation?

If the data is skewed as mean and standard deviation are affected by extreme values