Y1 Stats

Population

Entire set of relevant items (sampling units) being studied

Census (pros vs cons)

• Accurate (+)

• Expensive (-)

• Some testing destroys the item e.g. life of a battery (-)

Sampling frame

List of sampling units

Difference between population and sampling frame

Population is what you want to study, sampling frame is what you actually study

Simple random sampling (definition & pros vs cons)

Equal chance of being selected, use RNG alongside sampling frame

• Bias free (+)

• Sampling frame required (-)

Systematic sampling (definition & pros vs cons)

Takes every kth unit, pick random number between 1 and k for start point

• Quick to use (+)

• Sampling frame required (-)

Stratified sampling (definition & pros vs cons)

Proportionally represents strata (groups) in the sample to reflect the population, use either simple random or systematic to fill the groups

• Reflects population (+)

• Need clear strata for population (-)

Opportunity sampling (definition & pros vs cons)

Sample based on who/what is available

• Easy/cheap (+)

• No sampling frame needed (+)

• Unlikely to be representative (-)

Quota sampling (definition & pros vs cons)

Starts with quotas to be filled, but not necessarily representative of the population (groups filled using opportunity sampling)

• No sampling frame needed (+)

• Not random, potential bias (-)

Reasons why binomial distribution is appropriate

FFIT

1. Fixed number of trials

2. Fixed probability

3. Independent trials

4. Two outcomes, success or failure

Why [variable] data must be cleared

Trace (convert to numbers before calculating)

Linear interpolation assumption & why doesn’t hold in large data set

Spacing within classes equally distributed & most data = 0

Large data set: shows change in daily mean visibility over …

Time of sunshine

Continuous variable

A measured variable which can take any value

Interpret 3.1 in “y = 3.1x + c”, y = energy released (Joules), x = temperature (*C)

The increase in energy released is 3.1 Joules for each degree of temperature.

Can you find x when y = 150

No, this regression line is for x on y

Suitable value of the median of:

1. Daily mean pressure

2. Daily total rainfall

3. Daily mean temperature

4. Daily mean windspeed

5. Daily total sunshine

6. Humidity

7. Visibility

8. Daily cloud cover

1. 1000 hPa

2. 0.06-0.07 mm

3. 16-17*C

4. 6-7 knots

5. 6-7 hours

6. 80%

7. 3000 Dm (1Dm = 10m)

8. 6-7 Oktas

Suitable value of the range of:

1. Total rainfall

2. Total sunshine

3. Windspeed

4. Maximum gust

5. Pressure

1. 100mm

2. 16-17 hours

3. 23 knots

4. 90 knots

5. 25 hPa

What do m and n do: P = mX + nY

Multipliers for X and Y