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

ECON120321.jpg

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

ECON120322.jpg

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

ECON120323.jpg

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.

  • Median is the 50th percentile
    • INTER-QUARTILE RANGE = Q3 (75th percentile) – Q1 (25th percentile)
  • Locating Percentiles: ECON1203210.jpg
    • Where 'n' is the number of values and 'p' is the percentile

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)

ECON120324.jpg

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

ECON120325.jpg

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

ECON120326.jpg

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

The Least Squares Line

  • Line - ECON1203211.jpg
  • 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

ECON120327.jpg

End

This is the end of this topic. Click here to go back to the main subject page for Business and Economic Statistics.

References

Textbook refers to Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition,.

  1. Textbook Pg. 98-108
  2. Textbook Pg. 108- 117
  3. Textbook Pg. 117-126
  4. Textbook Pg. 126-144
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