Describing Data

[Graphically]
1. Frequency distribution(table)
2. Bar chart(discrete)
3. Histogram(continuous)
4. Frequency polygon
5. Scatter(Dot) plot
6. Pareto chart

Pareto chart

• Pareto Principle = "80-20 rule"
  • The majority of "result" is caused by small portion of the "factors"
    • eg., 80% of crimes are committed by 20% of criminals

Determination of class interval

• 2^k rule (recommended) : 2^k > number of observations
• interval i >= (H-L)/k

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[Numerically]

• Central tendency: Typical value representing the data set
  • 1. mean 2. median 3. mode
• Dispersion
  • 1. variance 2. standard deviation

Chebyshev's Theorem

• For any set of data, at least 1-(1/k^2) of the data lie with in +-k standard deviation from the mean(where k > 1)

Emperical rule

• For a bell shaped data mounded, Normal distribution
• Symmetric

Why dispersion?

1) enables us to compare the spread in two or more distributions.
2) tells the spread of the data

• A large measure of dispersion indicates the mean is not reliable.
• A small value for a measure of dispersion indicates data are focused around the mean.

Why standard deviation?

1) Provides meaningful comparison among different sets of data.

• tells weather data are wide-spread or focused around the mean.

2) Provides measurement of uncertainty.

• large SD tells there's high degree of uncertainty.
• small SD tells there's low degree of uncertainty.

3) Provides the population proportion of the data values.

Measures of position

• Quartiles, Decile, Percentile
• Location of Percentile = (n+1) x P/100