# Topic 2 - Measures Of Central Tendency, Variability and Linear Relationships

## Contents

Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition, pp. 98-144.

## Measures of Central Location/Tendency

### 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

### 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

### 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)

### 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

## End

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