Impact of extreme observations on measures of central tendency

Measures of central tendency are statistical tools that are used to determine the center of a data set. The three most commonly used measures of central tendency are the arithmetic mean (AM), the median, and the mode. These measures are used to summarize a data set and provide information about its distribution. In this context, the question is whether the presence of extreme observations affects these measures of central tendency.

Arithmetic Mean (AM)

The arithmetic mean is the sum of all the observations in a data set divided by the number of observations. The mean is influenced by extreme observations because it takes into account the value of every observation in the data set. Extreme observations can significantly affect the mean, especially if they are much larger or smaller than the other observations in the data set. For example, if a data set contains the values 1, 2, 3, 4, 5, and 100, the mean would be significantly higher than if the value of 100 were excluded.

Median

The median is the middle value in a data set when the observations are arranged in order. The median is not affected by extreme observations as it only considers the value of the middle observation(s) in the data set. For example, if a data set contains the values 1, 2, 3, 4, 5, and 100, the median would be 3.5 (the average of 3 and 4) and would not be significantly affected by the value of 100.

Mode

The mode is the value that occurs most frequently in a data set. The mode is not affected by extreme observations as it only considers the frequency of each value in the data set. For example, if a data set contains the values 1, 2, 3, 4, 5, and 100, the mode would be 1, 2, 3, 4, or 5 (depending on which value occurs most frequently) and would not be affected by the value of 100.

Conclusion

In conclusion, the presence of extreme observations can affect the arithmetic mean but not the median or mode. Therefore, it is important to consider the presence of extreme observations when using the arithmetic mean as a measure of central tendency, and to use the median or mode when extreme observations are present.