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

# Relative Locations of Mean, Median and Mode

The skewness of a distribution can have an impact on the location of mean, median and mode.

The relative locations of these measures on symmetric, negatively skewed, and positively skewed distributions are shown below. We have assumed a unimodal distribution, i.e., it has only one mode.

### Symmetric Distribution

**Mode = Median = Mean**

### Negatively Skewed Distribution

**Mode > Median > Mean**

### Positively Skewed Distribution

**Mode < Median < Mean**

Remember that skewness pulls the mean in the direction of the skew. Median is always between mean and mode.

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