General:
1) Watch out for questions about finding probability that could be referring to binomial
probability to calculate it. See if it has the conditions for binomial, like only 2
outcomes, independent outcomes etc.
2) Give probabilities to 4s.f./4d.p.
3) If asked why a model isn’t suitable, use your knowledge of the context to answer.
E.g., the temperature of a cup of water won’t continue decreasing forever. It will stay
the same at room temperature
4) If asked to find the range of values of something, think about what the lower limit
could be depending on context e.g., 0 and what the upper limit could be.
5) When finding the change in something, mention if it is a decrease or increase
6) To say why a model doesn’t work, look for values where the model wouldn’t hold, and the
conditions of values in the question/from the context of the question
7) Just put data into your calculator to work out statistics like mean, median, quartiles,
standard deviation etc.
8) Acceptance region is the region that's not the critical region. If the value fell in the
acceptance region, you accept the null hypothesis
AS Linea:
Sampling:
1) Sampling: a larger sample is needed for a population that is more varied than a
uniform population. Different samples can result in different results due to natural
variation in the population.
2) Individual units of a population are called the sampling units. A numbered list of
sampling units of a population is the sampling frame
3) Data collected can be quantitative or qualitative. Quantitative refers to a numerical
amount. Qualitative, we are looking for non-numerical values
4) Random sampling methods:
- Simple random: organise sampling units in a sample frame. Use a random number
generator to obtain sampling units to sample. Easy and cheap for small samples but
may not be large enough and a sampling frame is needed. Or lottery sample by
placing all units in a hat and picking them out at random.
- Systematic: organise sampling units in a sample frame. Choose a random starting
point and choose units at regular intervals. Simple and quick to implement but may
, coincide with a pattern, leading to an unrepresentative sample and also requires a
sampling frame
- Stratified: Divide population into mutually exclusive strata. Take a simple random
sample from each stratum, which the proportions of each stratum the same as in the
whole population. Can accurately reflect the structure of the population and give
representation to different groups in a population, but the population has to be
divided into distinct strata which can be costly. Also has all the disadvantages of
simple random sampling by selecting within each stratum
- Cluster: Sample clusters from the population. Randomly select clusters and sample
all units within chosen clusters. Random selection of clusters so unbiased BUT
differences between clusters may exist (e.g., regional similarities and differences)
which may distort the sample
= The 2 main ways to choose the numbers are: random number generator and lottery
sampling (where members of the sampling frame are written as tickets and placed into a
‘hat’ and the required number of tickets are drawn out)
5) Non random sampling methods:
- Quota: Same as stratified but sampling units are allocated to their quota group
(subsects of the population created by the interviewer) and assessed. Once the
quotas are full and units are non-randomly selected, the sample is finished. Doesn’t
require a sampling frame and can help for easy comparison between different
groups, reflecting the characteristics of the whole population. But it needs
populations to be divided into groups which may be inaccurate. It can introduce bias
as it is not random. How to take a quota sample (model answer):
- Opportunity: Determine sample size and criteria. Sample units available at the time
of sample. Easy and cheap to carry out but may not give a representative sample as it
may introduce bias from the sample conductor
, 6) Census (Sampling method): all sampling units have data collected. Perfectly
representative of the population. BUT it might be expensive, time-consuming, may
be bad because it may destroy the sampling units so it cannot be used
7) To use calculator to do standard deviation/mean of tables: statistics (6), 1-variable
and add all the values. If it’s grouped frequency, put the middle value of the groups
in the x section. Make sure frequency is turned on (shift + setup + 3 (statistics) +
frequency on) and add all the frequencies. Press AC then option + 2 to get the
statistics
8) Before using linear interpolation, make sure the class boundaries overlap
9) Linear interpolation assumes readings in each class are evenly spread
10) You can’t use the regression line to predict values of the independent variable using
the dependent variable
11) A varied population needs a larger sample
12) Different samples may give different results due to natural variation within the
population
Probability:
1) Mutually exclusive events (Events have no common outcome): P(A or B) = P(A) +
P(B) – Venn diagrams won’t intersect
2) Independent events (one event happening does not impact the probability of
another event happening): P(A and B) = P(A) x P(B)
3) If asked to find a change in something, say ‘increase of/decrease of’
4) Probability: P(A’ and B) means just the B part with no intersection, any of the A or
any of the ‘nothing’ part
5) Problems with modelling with probability: may assume events are independent
and do not affect each other (although they might), sample may not be large
enough to be representative
6) For probability distributions, a cumulative distribution would essentially be
adding up all the probabilities before it to get the next one. Other than that, it's a
normal probability distribution table
7) For cumulative distributions, the P(X <= final value that the variable could take) is
equal to 1
1) Watch out for questions about finding probability that could be referring to binomial
probability to calculate it. See if it has the conditions for binomial, like only 2
outcomes, independent outcomes etc.
2) Give probabilities to 4s.f./4d.p.
3) If asked why a model isn’t suitable, use your knowledge of the context to answer.
E.g., the temperature of a cup of water won’t continue decreasing forever. It will stay
the same at room temperature
4) If asked to find the range of values of something, think about what the lower limit
could be depending on context e.g., 0 and what the upper limit could be.
5) When finding the change in something, mention if it is a decrease or increase
6) To say why a model doesn’t work, look for values where the model wouldn’t hold, and the
conditions of values in the question/from the context of the question
7) Just put data into your calculator to work out statistics like mean, median, quartiles,
standard deviation etc.
8) Acceptance region is the region that's not the critical region. If the value fell in the
acceptance region, you accept the null hypothesis
AS Linea:
Sampling:
1) Sampling: a larger sample is needed for a population that is more varied than a
uniform population. Different samples can result in different results due to natural
variation in the population.
2) Individual units of a population are called the sampling units. A numbered list of
sampling units of a population is the sampling frame
3) Data collected can be quantitative or qualitative. Quantitative refers to a numerical
amount. Qualitative, we are looking for non-numerical values
4) Random sampling methods:
- Simple random: organise sampling units in a sample frame. Use a random number
generator to obtain sampling units to sample. Easy and cheap for small samples but
may not be large enough and a sampling frame is needed. Or lottery sample by
placing all units in a hat and picking them out at random.
- Systematic: organise sampling units in a sample frame. Choose a random starting
point and choose units at regular intervals. Simple and quick to implement but may
, coincide with a pattern, leading to an unrepresentative sample and also requires a
sampling frame
- Stratified: Divide population into mutually exclusive strata. Take a simple random
sample from each stratum, which the proportions of each stratum the same as in the
whole population. Can accurately reflect the structure of the population and give
representation to different groups in a population, but the population has to be
divided into distinct strata which can be costly. Also has all the disadvantages of
simple random sampling by selecting within each stratum
- Cluster: Sample clusters from the population. Randomly select clusters and sample
all units within chosen clusters. Random selection of clusters so unbiased BUT
differences between clusters may exist (e.g., regional similarities and differences)
which may distort the sample
= The 2 main ways to choose the numbers are: random number generator and lottery
sampling (where members of the sampling frame are written as tickets and placed into a
‘hat’ and the required number of tickets are drawn out)
5) Non random sampling methods:
- Quota: Same as stratified but sampling units are allocated to their quota group
(subsects of the population created by the interviewer) and assessed. Once the
quotas are full and units are non-randomly selected, the sample is finished. Doesn’t
require a sampling frame and can help for easy comparison between different
groups, reflecting the characteristics of the whole population. But it needs
populations to be divided into groups which may be inaccurate. It can introduce bias
as it is not random. How to take a quota sample (model answer):
- Opportunity: Determine sample size and criteria. Sample units available at the time
of sample. Easy and cheap to carry out but may not give a representative sample as it
may introduce bias from the sample conductor
, 6) Census (Sampling method): all sampling units have data collected. Perfectly
representative of the population. BUT it might be expensive, time-consuming, may
be bad because it may destroy the sampling units so it cannot be used
7) To use calculator to do standard deviation/mean of tables: statistics (6), 1-variable
and add all the values. If it’s grouped frequency, put the middle value of the groups
in the x section. Make sure frequency is turned on (shift + setup + 3 (statistics) +
frequency on) and add all the frequencies. Press AC then option + 2 to get the
statistics
8) Before using linear interpolation, make sure the class boundaries overlap
9) Linear interpolation assumes readings in each class are evenly spread
10) You can’t use the regression line to predict values of the independent variable using
the dependent variable
11) A varied population needs a larger sample
12) Different samples may give different results due to natural variation within the
population
Probability:
1) Mutually exclusive events (Events have no common outcome): P(A or B) = P(A) +
P(B) – Venn diagrams won’t intersect
2) Independent events (one event happening does not impact the probability of
another event happening): P(A and B) = P(A) x P(B)
3) If asked to find a change in something, say ‘increase of/decrease of’
4) Probability: P(A’ and B) means just the B part with no intersection, any of the A or
any of the ‘nothing’ part
5) Problems with modelling with probability: may assume events are independent
and do not affect each other (although they might), sample may not be large
enough to be representative
6) For probability distributions, a cumulative distribution would essentially be
adding up all the probabilities before it to get the next one. Other than that, it's a
normal probability distribution table
7) For cumulative distributions, the P(X <= final value that the variable could take) is
equal to 1
