When considering measures of variation that are sensitive to extreme values, it's important to understand how each measure is calculated and how it responds to changes in the data set, particularly extreme values (outliers).
1. Range: This is calculated as the difference between the maximum and minimum values in a data set. Because it only considers these two values, any extremely high or low value will directly affect the range, making it the most sensitive to extreme values.
2. Median: This is the middle value when the data is ordered from smallest to largest. If there are an odd number of data points, it's the central value; if even, it's the average of the two central values. The median is resistant to extreme values because it only depends on the middle of the data set rather than the extremes.
3. Histogram: This is not a measure of variation; it's a type of graph that displays the distribution of data. It shows the frequency of data points within certain ranges but does not provide a single value for variation.
4. Mean: Also known as the average, this is calculated by adding up all the values and dividing by the number of values. While the mean is affected by extreme values because they contribute to the total sum, it does not change as drastically as the range when an extreme value is present.
In summary, the measure of variation most sensitive to extreme values is the Range.
Correct answer: Range
