Measures of Center (College Board AP® Statistics)

Mode

What is the mode?

• The mode is the value that occurs most often in a data set

  • It is possible for there to be more than one mode

  • It is possible for there to be no mode

• The mode can appear at any point in the distribution of the data set

  • It is not necessarily in the center of the distribution

• The mode is the only measure of center that can be used for categorical data (e.g. favourite colour)

Median

What is the median?

• The median is the middle value when the data is in order of size

  • If there are an odd number of values in the data set

    • then the median is the data value in the center of the set

  • If there are an even number of values in the data set

    • then there are two values in the middle and the median is the midpoint of these two values

How do I find the median for ungrouped data?

• For a data set that contains values

  • the middle value will be located at the position

• The median is a resistant statistic

  • It is not affected by extreme values

  • It is a suitable measure of center for distributions that are

    • either approximately symmetrical

    • or strongly skewed with outliers

Mean

What is the mean?

• The mean is the sum of all the values divided by the number of values in the data set

  • It uses all values in a data set

• If the distribution of the data is approximately symmetrical

  • the median and the mean will be close in value

    • and both values will be representative of the population

• If the distribution of the data is strongly skewed or has outliers

  • The mean will be affected by the extreme values

    • It is therefore not a resistant statistic

How do I find the mean for ungrouped data?

• The formula for calculating the mean is given to you in the exam

  • 

  • Where is the sum of the pieces of data