**Quantitative Data Analysis – Normal and Skewed Distributions**

**(1) Normal Distribution:**

Classic bell shaped curve, it is the predicted distribution when using equally likely sets of results. For example, if a light bulb has a lifetime of 100 hours we would expect some bulbs to last a little longer than 100 hours and some to last a little less.

**Characteristics of a Normal Distribution:**

– The three measures of **central tendency, mean, median and mode** are all in the exact mid-point (the middle part of the graph/the peak of the curve).

– The distribution is symmetrical.

**(2) Skewed Distribution**

This occurs when the scores are not equally distributed around the mean.

*Positive Skew* – The best way to imagine the shape of a positive skew is to think of the scores on a very difficult exam, were few people got a high mark being plotted on a graph. Most of the scores would lie to the *left side* of the x axis with fewer scores being plotted at the higher end of the x axis (the right).

**Revision Tip** – When thinking of the shape of a **positive skewed distribution, **think of the shape of your **right foot. **

*Characteristics of a Positive Skewed Distribution Graph:*

– Central tendency order is plotted mode, median followed by the mean.

**Negative Skew** – The best way to remember the shape of a negative skewed is to imagine the scores on a very easy exam, were few people got a low mark, were plotted on a graph. In this situation, people would obtain a higher score and therefore, most scores would sit to the *right* side of the x axis with fewer scores sitting to the left side of the x axis.

**Revision Tip:** When thinking of the **shape a of negative skewed distribution,** think of the shape of your **left foot.**

*Characteristics of a Negative Skewed Distribution Graph:*

– Central tendency order is plotted mean, median followed by the mode.

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