Topic 2 - Measures Of Central Tendency, Variability and Linear Relationships
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This article is a topic within the subject Business & Economic Statistics.
Contents |
Required Reading
Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition, pp. 98-144.
Measures of Central Location/Tendency
^{[1]}
Arithmetic Mean - Average
- This can only be used for interval data
Median
- Middle Number (of the data)
- Can be used for interval and ordinal data but not nominal
Mode
- Greatest frequency
- Can be used for all types of data
Which is Best?
- Mean is generally first selection, however median is not as sensitive to extreme values
- Mode is seldom the best
Measures of Variability
^{[2]}
Range
- Max Value - Min Value
Variance
- Population Variance
- Sample Variance
Standard Deviation
- Square root the Variance = ‘σ’ or ‘S’
Z Score
- Z = (Observation – Mean) / Standard Deviation
Coefficient of Variation
- removes impact of differing magnitude of numbers - it is a relative measure of variability
Measures of Relative Standing And Box Plots
^{[3]}
Percentiles
Percentiles is a ranking of data whereby P percent of observations are lower than that value.
Box Plots
- Inputs: Min, Max, 1st/2nd/3rd Quartiles
- 'Whiskers' extend outwards to the most extreme point that is not an outlier
- Outliers are considered to be the 1st Quartile MINUS OR 3rd Quartile PLUS 1.5 * Inter-quartile range)
Measures of Linear Relationships (Bivariate Analysis)
^{[4]}
Covariance
- Sign determines +/-/no linear relationship Magnitude determines strength
- If positive (negative) numbers it’s a positive (negative) linear relationship
Coefficient of Correlation
- Covariance / SD(X)*SD(Y) - where SD(X) is the standard deviation of 'X'
- Judged in relation to:
- -1 = perfect negative relationship
- 0 = no linear relationship)
- 1 = positive linear relationship
Coefficient of Determination - 'R'
- It is the Coefficient of Correlation SQUARED
- E.g. if S(x,y) = .87 than R^2 = .7588 (75.88% of the variation is explain by the other variable)
- PLEASE NOTE: Correlation is not Causation - there can be confounding factors
- E.g. Mobile Phones & Cancer. There are more mobile phone users in the city which would give them more exposure to radiations
- PLEASE NOTE: Correlation is not Causation - there can be confounding factors
The Least Squares Line
- Line -
- B0 & B1 chosen to minimize e(1,2…n) where e(1]^2 = (y1-y^)^2
- More on this later in the course within the topic of Regression
End
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References
Textbook refers to Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition,.