The measure of variation which is least affected by extreme items is:

The answer is (b) Quartile deviation.

Explanation:

Variation is the dispersion of data points from the central tendency. It indicates how much the data points are spread out from the central value. There are different measures of variation, such as range, quartile deviation, mean deviation, and standard deviation. Each measure has its advantages and limitations.

When data points are symmetrically distributed, all measures of variation yield similar results. However, when data points are skewed or contain extreme values, some measures of variation may be affected more than others.

Range:

The range is the simplest measure of variation. It is the difference between the highest and lowest values in the data set. The range is easy to compute but is sensitive to extreme values. A single extreme value can greatly influence the range and make it an unreliable measure of variation.

Quartile Deviation:

Quartile deviation is a measure of variation that is less affected by extreme items. It is the difference between the upper quartile (Q3) and the lower quartile (Q1). The quartile deviation is less sensitive to extreme values because it only considers the middle 50% of the data. It is a robust measure of variation and is useful when the data set contains outliers.

Mean Deviation:

Mean deviation is the average of the absolute deviations of each data point from the mean. It is less sensitive to extreme values than the range but more sensitive than the quartile deviation. Mean deviation is not widely used because it is difficult to compute and interpret.

Standard Deviation:

Standard deviation is the most commonly used measure of variation. It is the square root of the variance, which is the average of the squared deviations of each data point from the mean. Standard deviation is sensitive to extreme values and can be affected by outliers. However, it is a powerful tool for statistical analysis and provides valuable information about the spread of data.

Conclusion:

In conclusion, quartile deviation is the measure of variation that is least affected by extreme items. It is a robust measure of variation that is useful when the data set contains outliers. Although other measures of variation may be more commonly used, it is important to choose the appropriate measure based on the characteristics of the data set.

B) Quartile deviation