Lessons

- Descriptive Vs. Inferential Statistics
- Types of Measurement Scales
- Parameter, Sample Statistic, and Frequency Distribution
- Relative Frequencies and Cumulative Relative Frequencies
- Properties of a Data Set (Histogram / Frequency Polygon)
- Measures of Central Tendency
- Calculating Arithmetic Mean
- Calculating Weighted Average Mean
- Calculating Geometric Mean
- Calculating Harmonic Mean
- Calculating Median and Mode of a Data Set
- Quartiles, Quintiles, Deciles, and Percentiles
- Range and Mean Absolute Deviation
- Variance and Standard Deviation
- Chebyshev’s Inequality
- Coefficient of Variation
- Sharpe Ratio
- Skewness and Kurtosis
- Relative Locations of Mean, Median and Mode

# Types of Measurement Scales

Depending on the information we want the data to represent, we can choose one of the four measurement scales.

**Nominal Scale**

- Used to classify data
- Observations are put into categories based on some criteria.
- The category labels can be numbers but they don’t have any numeric value.
- Example 1: Classifying stocks as small-cap, mid-cap, and large-cap
- Example 2: Classifying funds as equity funds, debt funds, and balanced funds.

**Ordinal Scale**

- Used to classify and order (Ranking)
- Observations are not just classified but also ordered
- Example: Ranking top 10 stocks based on their P/E ratio
- The numbers only represent the order. They do not say anything about how much better or worst a stock is at a given number compared to one at a lower number.

**Interval Scale**

- Used to classify and order with an equal interval scale
- The intervals between adjacent scale values are equal.
- Scale has an arbitrary zero point and as a result you cannot calculate ratios.
- Example: Temperature scales. A temperature of 40 degrees is higher than 35 degrees and is higher by 5 degrees.
- The problem is that a temperature of 0 degrees does not imply absence of temperature. Because of this, a temperature of 20 degrees does not necessarily mean twice as hot as a temperature of 10 degrees.

**Ratio Scale**

- All the above features along with an absolute zero.
- Equal units of measurements and a rational zero point for the scale.
- Example: Income of a group of people in dollars. If you have 0 dollars that means complete absence of money (what we are measuring). However, if A has $10 and B has $20, then B has twice as much money as A has.

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