Mode and Median | StudyTution

October 26, 2020 Mehak Statistics 0

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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