Questions: In which of these cases should the median be used? When the data has small variance When the data has extreme values When the data has nominal values When data has no outliers

In which of these cases should the median be used?
When the data has small variance
When the data has extreme values
When the data has nominal values
When data has no outliers

Transcript text: In which of these cases should the median be used? When the data has small variance When the data has extreme values When the data has nominal values When data has no outliers

Solution

Solution Steps

Step 1: Identify the Purpose of the Median

The median is a measure of central tendency that is used to identify the middle value in a data set. It is particularly useful in situations where the data may be skewed or contain outliers.

Step 2: Analyze the Options

When the data has small variance: The median is not specifically required for small variance; the mean can also be appropriate.
When the data has extreme values: The median is preferred because it is not affected by extreme values or outliers, unlike the mean.
When the data has nominal values: The median is not applicable to nominal data, as nominal data is categorical and does not have a meaningful order.
When data has no outliers: The mean can be used effectively when there are no outliers, as it will not be skewed by extreme values.

Step 3: Select the Appropriate Case

Based on the analysis, the median should be used when the data has extreme values, as it provides a better measure of central tendency in the presence of outliers.

Final Answer

The median should be used when the data has extreme values.

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