Asked Jul 16, 2019

What happens to the variance when outliers are eliminated replaced by values closer to the mean


Expert Answer

Step 1



Mean is an important measure of center when the data is quantitative. Mean of a data set is the sum of the data set divided by the size.


The variance is based on how much each observation deviates from a central point represented by the mean. In general, the greater the distances between the individual observations and the mean, the greater the variability of the data set.

The variance and standard deviation increases with the increase in the distances between the individual observations and the mean of the data set.

In other words, it can be said that, variance is the average of squared difference of data from the mean. The formula for variance is different in case of sample and population.


The outlier is the observational point that is distant from the remaining observational points. In other words outlier is an observation that lies in an abnormal distance from the remaining values.

Step 2

Formulae to obtain variance:

The general formula to obtain the sample variance and population variance are given below:


Image Transcriptionclose

Σx-3) x's are the observai ons in the sample dataset, Sample variance(s2)= i-l xis the sample mean, n-1 n is the sample size. (X;'s are the observaions in the population, Σ(x-μ Popul ati on variance (o2): uis the population mean, Nis population size

Step 3


Outliers are the observations that are in distant from the remaining observations. When outliers are eliminated and replaced by the values closer to the mean, the average of squared difference of data from the mean will decrease.

That is, by replacing the outliers with the values closer to the mean, the values of (xi–mean) will decrease.

Therefore, (xi...

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