Which is preferred as measure of central tendency if the data is highly skewed.Review LaterMeanMedianModeRange

1. Break Down the Problem

To determine which measure of central tendency is preferred for highly skewed data, we will evaluate each option: Mean, Median, Mode, and Range.

2. Relevant Concepts

• Mean: The average of all data points, sensitive to outliers.
• Median: The middle value when the data is arranged in order, not influenced by extreme values.
• Mode: The most frequently occurring value in the dataset.
• Range: The difference between the highest and lowest values, not a measure of central tendency.

3. Analysis and Detail

1. Mean: In highly skewed distributions, the mean can be misleading as it gets pulled in the direction of the skew.
2. Median: This is generally the most reliable measure in skewed distributions since it represents the middle value, showing where the bulk of the data lies.
3. Mode: This can also be useful, particularly in categorical data, but it does not provide a central point for numerical datasets.
4. Range:While it provides information about spread, it does not convey central tendency as it only focuses on the extremes.

4. Verify and Summarize

In summary, the median is statistically the most suitable measure of central tendency for highly skewed datasets. This is because it accurately reflects the center of the data without being distorted by outliers.

Final Answer

Median is preferred as the measure of central tendency when the data is highly skewed.