Statistics 1 Wordy Questions

Give reasons why a statistical model is used.
To simplify a real world problem, to improve understanding of a problem, to describe a problem, quicker/cheaper than using the real thing, allows predictions about future outcome to be made, refining the model and changing the parameters is possible.
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Give an example of a variable that can be modelled by a normal distribution
Height, weight
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Give an example of a random variable that could be modelled by a discrete uniform distribution
Score on a face after tossing a fair die
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Comment on the assumption that two events are independent
If the events are correlated, the assumption of independence is not sensible
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Comment on the assumption of normality
Normal must use continuous data, so if the data is discrete, the assumption is not very good
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X is normally distributed with mean μ and variance σ^2. What are the properties of the distribution of X?
Symmetrical about the mean, mode=mean=median, horizontal axis asymptotic to curve, 95% of data lies within 2s.ds of the mean
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How do you prove events are statistically independent?
P(AnB)=P(A)xP(B) or P(B|A)=P(B)
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How can you tell if events are mutually exclusive?
They can't happen at the same time so P(AnB)=0
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Explain the meaning of a 'sample space'
A list of all possible outcomes of an experiment
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Explain the meaning of an 'event'
A sub-set of outcomes of an experiment
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Explain the skewness of the data
Use Q3-Q2 and Q2-Q1
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Is normal distribution suitable?
If the skewness if only very small or the data is symmetrical, then yes.
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When should the median be the average used?
For quantitative data, when data is skewed and when there might be extreme values
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Disadvantages of a statistical model
Only give a partial description of the real situation and only work for a restricted range of values
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Stage 1 of Statistical Model
A real world problem is observed
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Stage 2 of Statistical Model
A mathematical model is devised
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Stage 3 of Statistical Model
The mathematical model is used to make predictions about the expected behaviour of the real world problem
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Stage 4 of Statistical Model
Experimental data is collected from the real world
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Stage 5 of Statistical Model
Compare the predicted and observed outcomes
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Stage 6 of Statistical Model
Statistical tests are used to asses how well the model describes the real world
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Stage 7 of Statistical Model
The mathematical model is refined, if necessary, to improve the match of the predicted outcomes with observed (experimental) data
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What does each bar represent in a histogram?
The area is proportional to the frequency
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Why are histograms used?
If the variable is continuous, then histograms are good to use
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When should the mean be used as a measure of average?
For quantitative data as all pieces of data are used. However, should only be used if the data is fairly symmetrical as the mean could not be affected by extreme values.
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When should the mode be used as a measure of average?
If the data is qualitative or if quantitative with a clearly defined mode. It is not very useful if the distribution is fairly even.
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What should you talk about when commenting on dispersion
Talk about skewness, IQR and quartiles
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Card 2

Front

Give an example of a variable that can be modelled by a normal distribution

Back

Height, weight

Card 3

Front

Give an example of a random variable that could be modelled by a discrete uniform distribution

Back

Preview of the front of card 3

Card 4

Front

Comment on the assumption that two events are independent

Back

Preview of the front of card 4

Card 5

Front

Comment on the assumption of normality

Back

Preview of the front of card 5
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