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Business Statistics 1 (QM161) Statistics Formulas Cheat Sheet

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Sandra Watson
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University of New England (Australia)

Business Statistics 1 (QM161)

TOPIC 2 SURVEYS AND SAMPLING
Population parameters: measurements based on the entire population (requires census) e.g.
Proportion of US adults who believe that global warming is primarily anthropogenic.
Sample Statistics: measurement based on a sample of the population *changes when we change our
sample. Could be %.
Each statistic is an estimate of a population parameter.
Process of sample surveys: Determine exact objective-Know what the population is- Determine
sampling frame (list of those within population that can be sampled)- Draw target sample (contact
people)- Actual sample (people that responded)- Statistical analysis
SAMPLING METHODS/DESIGN
Simple Random Sample (SRS): A sample drawn so that every possible sample has the same
chance of being selected. Dis-advantage: ignores diff proportions of individuals in population. (not
representative)
Stratified Sampling: Divide into diff groups of similar individuals (STRATA) and take SRS from
each group. STRATA: Homogenous group. E.g. BES student’s degrees (commerce, economics,
other)
Cluster Sampling: Choose groups or clusters at random from population and take census from
these groups. Clusters should be different within and similar in between. E.g. BES classes are
clusters.
Systematic Sampling: Use fixed interval on our sampling frame. E.g. Every 4th student enrolled in
BES. Disadvantage: not representative
Multi-stage sampling: Combination of sampling methods.
SAMPLING ERRORS/BIAS
Sampling error (unavoidable): difference between statistic and parameter due to random process.
Can decrease error by increasing sample size. *no sampling error in census
Bias (non-sampling error): due to bad sampling method. *could exist in census
Voluntary response bias (volunteer response sample): general announcement made, individuals
decide if they participate.
Non-response bias: When the response is biased based on some people were excluded or chose not
to respond and may have similar characteristics.
Response bias: Anything that may influence the answer they give. Push polling: “do you like
BES?” instead of “opinion on BES?”
Convenience Frame: only include individuals who are convenient (out the front of the shop)
Bad sampling frame: e.g. Used 2nd year bes students to predict 1st yr bes marks. *people didn’t
continue =bias
TOPIC 3 DISPLAYING & DESCRIBING categorical DATA
Relative frequency: just frequency as %
Find freq. from relative freq: 11.7% of all individuals (623) were females; 11.7%xn (11.7×623=73
were females)
Bar chart: must have gaps in categorical data. LABEL title, categories bottom (x axis), Freq on left
axis.
Side by side bar chart: bar chart for contingency tables (female/male data next to each other for
each category)
Stacked bar chart: in order stack categories on top of each other. Each will reach 100% unless
rounded up/down in working out.
“AREA PRINCIPLE” – image should reflect size/number for each category. Bad graphical
displays do not follow principle. (If you make a pic twice as high and twice as wide it has 4 times
the area)

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Business Statistics 1 (QM161) Statistics Formulas Cheat Sheet

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