Identify the measures of central tendency A. Arithmetic mean B. Median C.…

Concept

A measure of central tendency summarizes where observations in a distribution cluster around a representative central value.

The arithmetic mean, median, and mode locate a distribution through averaging, ordered position, and frequency, respectively.

Application

The arithmetic mean uses all observations in an average, the median uses the central ordered value, or averages the two central values when the count is even, and the mode uses the most frequent observation.

Contrast

• Range is the difference between the maximum and minimum observations, so it measures spread rather than location.

• The second decile is the value below which 20% of the ordered observations fall; it is a positional quantile, not the central 50th-percentile position.

Cross-check

A central-value measure should identify a typical or middle location. The maximum-minus-minimum width and the 20th-percentile cut point do not perform that role.

Result

Therefore, the measures are arithmetic mean, median, and mode, so the correct combination is A, B & D only.