Numaracy for the Business Environment

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2. • Statistics is the science of data collection,
organising and interpreting numerical facts.
• Gaining information from numerical data or
making sense of data.
• Descriptive Statistics
– Organising and summarising data – condense large
volumes of data into a few summary measures.
• Statistical inference
– Generalises subset data findings to the broader
universe.
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3. • Statistical analysis in management decision-making
Input Process Output
→
Statistical Decision
→ Data → → Information →
Analysis Making
→
Useful,
Raw Transformation
Usable
Observations Process
Meaningful
MANAGEMENT DECISION SUPPORT SYSTEM
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4. • Approach for the Statistical process
Research process
becoming a cycle
PLANNING
DECISION- DATA
MAKING COLLECTION
Primary and
Descriptive Statistics
secondary
Statistical inference
sources
EDITING
CONCLUSIONS
and CODING
ANALYSIS
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5. • Basic concepts of Statistics
– Parameter
• Computed from the universe.
– Statistic
• Computed from the subset taken from the universe.
– Variable
• Characteristic of the item being observed or measured.
– Data
• Collection of observations on one or more variable.
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6. • Basic concepts of Statistics
– Population
• Entire group we want information about.
– Sample
• The proportion of the population we actually examine.
• Representative and not biased.
• Random sampling.
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7. • Basic concepts of Statistics
– Census
• Investigate the whole population
• Expensive
• Time consuming
• Sections of population is inaccessible
• Units are destroyed
• Inaccurate
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8. • Sampling methods
– Probability sampling
• Each element has a known probability of being
selected as part of sample.
• Unbiased inference about the population.
– Non-probability sampling
• Element from the population are not selected
random.
• The elements are selected without knowing the
probability of being selected as part of sample.
• We can not use results of these samples to make
conclusions about the population.
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9. • Sampling methods – Probability sampling
– Simple random sampling
• Number the elements of the population from
1 to N.
• Select a random starting point in the random table.
• From the starting point read systematically in any
direction.
• Divide the digits in the random table into groups
with the same number of digits as the number of
digits in the population size (N).
• Find n random numbers from 1 to N – no
duplicates.
• Identify each of the chosen random numbers in the
population. 9

10. • Sampling methods – Probability sampling
– Stratified random sampling
• Population heterogeneous with respect to the variable
under study.
• Population divided into N = N1 + N2 + ….. + Nk
homogeneous sub-
populations called strata. (k = number of stratum)
• Sample size form each n = n1 + n2 + ….. + nk
sample proportional to
(k = number of stratum)
stratum size.
• Draw a simple random sample N
from each of the stratum. n 
i n, i  1...k
i
N 10

11. • Sampling methods – Non-probability sampling
– Convenience sampling
• Not representative of the target population.
• Items being selected because they are easy to find,
inexpensive and self selected.
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12. • Sampling methods – Non-probability sampling
– Quota sampling
• Population divided into sub-classes according to a
certain characteristic.
• A non-sampling method is used to select a sample
from each stratum.
• It is a technique of convenience.
• Researcher attempts to fill the quota quickly.
• Sample is not representative of the population.
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13. • Sampling methods – Non-probability sampling
– Judgement sampling
• Elements from the population are chosen by the
judgement of the researcher.
• The probability that an element will be chosen cannot
be calculated.
• Sample is biased.
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14. • Sampling methods – Non-probability sampling
– Snowball sampling
• Is used where sampling units are difficult to locate
and identify.
• Find a person who fits the profile of characteristics
of the study.
• From this person obtain names and locations of
others who will fit the profile.
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15. DIFFERENT
TYPES OF
DATA
QUANTITATIVE QUALITATIVE
(numerical scale) (categorical)
Discrete Continuous
(integer) (any numerical value)
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16. DIFFERENT
TYPES OF
DATA
QUANTITATIVE QUALITATIVE
(numerical scale) (categorical)
Nominal Ordinal Interval Ratio
scaled scaled scaled scaled
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17. • Problems associated with the collection
of data:
– Characteristics have to be measured.
– Measurements can be complicated.
– Measurements must be valid and accurate.
– Secondary data not easy to validate.
– Data can be incomplete, typographical errors,
small sample.
– Biased or misleading responses.
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18. • Problems associated with the collection
of data:
– Make sure of the following:
• Who conducted the study?
• What data was collected?
• What sampling method was used?
• Sample size?
• Chance of bias?
• Is data relevant to the problem at hand?
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19. • How to design a questionnaire
– Questions should:
• Be simply stated.
• Have no suggestion of a specific answer.
• Be specific and address only one issue.
• Carefully word sensitive issues.
• Not require calculations or a study to be answered.
– Types of questions:
• Closed
• Open
• Combined
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20. • Appearance and layout of a questionnaire
– Attractive look.
– Coloured paper.
– Clear instructions on how to complete.
– Reasonably short.
– Enough space to complete questions.
– Mother-tongue language.
– Interesting questions first.
– Simple questions first, controversial questions later.
– Complete one topic before starting the next.
– Important information first. 20

21. • Interview
– Fieldworker completed questionnaire
• Higher response rate and data collection is immediate.
– Mailed questionnaires
• When population is large or dispersed.
• Low response rate.
• Time consuming.
– Telephone interview
• Lower costs.
• Quicker contact with geographically dispersed
respondents. 21

22. • Editing the data
– Obvious errors should be eliminated.
– Eliminate questionnaires that are incomplete
and unreliable.
– Questionnaires should be pre-tested on a small
group of people.
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