The mean is the best measure of central tendency because it__________

Analyze the question The question asks why the mean is considered the "best" measure of central tendency. We need the property that truly describes the mean.

Explain the concept The mean (arithmetic average) = (sum of all observations) ÷ (number of observations).

Key properties of the mean:

• It uses every value in the data set.
• The sum of deviations of all observations from the mean is zero, so it acts as the balancing point (like the fulcrum of a seesaw).
• It is affected by extreme values (outliers).
• It needs complete data, since every value must be included.

Check each option

• A. Can be calculated from incomplete data: False. The mean needs all values. The median or mode can sometimes be found with incomplete data, but not the mean.
• B. Is a balancing point in an observation: True. Deviations above the mean exactly cancel deviations below it: Σ(x − x̄) = 0.
• C. Is a midpoint value in an array of data: This describes the median, not the mean.
• D. Is not affected by extreme values: False. The mean is strongly affected by extremes. For example, for 2, 3, 4, 5, 100 the mean is 22.8, which is pulled far from the typical values. This is a weakness of the mean, and the median resists it better.

Answer

Tip Remember the matching words:

• Mean → Balance point (sum of deviations = 0)
• Median → Middle value
• Mode → Most frequent

If an option says the mean is "not affected by extreme values", it is a trap. That is a feature of the median.