**Mode**

The mode of a categorical variable is the most common category, the category with the highest frequency

**The mode labels**

- The longest bar in a bar chart
- The widest slice in a pie chart.
- In a Pareto chart, the mode is the first category shown.

**Example**

- Let consider the example A,A,B,C,A,D,A,B,C,C, A,B,C,D,A
- The longest bar in a bar chart
- The widest slice in a pie chart.
- The most common category is ”A”

**Bimodal and multimodal data**

- If two or more categories tie for the highest frequency, the data are said to be bimodal (in the case of two) or multimodal (more than two).
- Let consider the example A,A,B,C,A,C,A,B,C,C, A,C,C,D,A,A,C,D,B
- Both category ”A” and ”C” have highest frequency.

**Median**

- Ordinal data offer another summary, the median, that is not available unless the data can be put into order.
- The median of an ordinal variable is the category of the middle observation of the sorted values.
- If there are an even number of observations, choose the category on either side of the middle of the sorted list as the median.

**Example**

- Consider the grades of 15 students which is listed as A,B,B,C,A,D,B,B,A,C, B,B,C,D,A
- The ordered data is A,A,A,A,B,B,B,B,B,B,C,C,C,D,D
- The median grade is the category associated with the 8 observation which is ”B”.
- Consider the grades of 14 students which is listed as A,B,B,C,A,D,B,B,A,C, B,B,C,D
- The ordered data is A,A,A,B,B,B,B,B,B,C,C,C,D,D
- The median grade is the category associated with the 7 or 8 observation which is ”B”.
- Consider the grades of 15 students which is listed as A,B,B,C,A,D,B,B,A,C, B,B,C,D,A
- The ordered data is A,A,A,A,B,B,B,B,B,B,C,C,C,D,D
- The median grade is the category associated with the 8 observation which is ”B”.
- The most common grade is ”B”, hence mode is ”B”
- In this example both mode and median are the same.
- Consider the grades of 15 students which is listed as A,B,B,C,A,D,A,B,A,C,B,A,C,D,A
- The ordered data is A,A,A,A,A,A,B,B,B,B,C,C,C,D,D
- The median grade is the category associated with the 8 observation which is ”B”.
- The most common grade is ”A”, hence mode is ”A”
- In this example both mode and median are the different.

**summary**

- The mode of a categorical variable is the most common category.
- The median of an ordinal variable is the category of the middle observation of the sorted values.

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