Which of the following is least affected if an extreme high outlier is added to your data? (a) M

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Which of the following is least affected if an extreme high...

Key Concepts

Range

The range is a simple measure of variability defined as the difference between the maximum and minimum values in a dataset. It directly reflects the impact of extreme values; hence, the addition of an outlier can greatly expand the range, making it an unstable measure of dispersion in the presence of outliers.

Standard Deviation

Standard deviation is a measure of dispersion that quantifies the average distance of data points from the mean. Since it involves the mean in its calculation and squares the deviations, the presence of outliers can considerably inflate the standard deviation, affecting its reliability as a measure of spread.

Median

The median is a measure of central tendency that represents the middle value in a sorted dataset. It is considered robust because it is minimally affected by extreme values or outliers, making it a reliable indicator of the center even when the data contains anomalies.

Mean

The mean, or average, is calculated by summing all values and dividing by the number of observations. Although widely used, it is highly sensitive to outliers since an extreme value can skew the mean significantly, thus not always accurately representing the typical value of the dataset.

Outliers

Outliers are data points that deviate significantly from the overall pattern of a dataset. They can be extremely high or low compared to the rest of the data and have a disproportionate influence on statistical measures, potentially distorting the conclusions drawn from the data.

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