3.5:
Trimmed Mean
Generally, the mean of a dataset is calculated by dividing the sum of all values by the total number of values. However, the mean is very sensitive to the presence of extreme values. For example, the mean height of students is affected by the outliers—too short or too tall students.
In such cases, the data are first ordered and then the outliers removed. Now, the mean is calculated for the remaining data values. Such a mean is called the trimmed or truncated mean.
Notice that, here, from a total of ten data values, one from either side of the dataset is trimmed. That is, 10 percent of the data are removed from both the sides. Then, the mean is calculated for the remaining values and is called 10 percent trimmed mean.
Trimmed mean helps to avoid meaningless fluctuations in the mean. For example, the inflation rate is calculated using the trimmed mean of commodity prices. It ignores the high volatile price changes and smoothens the data, providing the most accurate inflation rate.
3.5:
Trimmed Mean
While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the problem. The trimmed mean is one such example. After sorting the data, the outliers can be removed before calculating the arithmetic mean, the geometric mean, or the harmonic mean. When trimming is carried out symmetrically on the same percentage of the arranged data from both the upper and lower bounds, the data is said to be trimmed by that percentage.