AVERAGEAVG

AVERAGEAVG is a term used in statistics and data analysis to denote a condensed representative value obtained by averaging multiple subpopulation means. It is commonly used when data come partitioned into groups, regions, or samples, and a single figure is needed for comparison or reporting.

Definition and calculation. There are two common variants. The unweighted AVERAGEAVG computes the arithmetic mean of the subpopulation means: AVERAGEAVG = (1/k) Σ m_i, where m_i is the mean of the i-th subgroup and k is the number of subgroups. The weighted form accounts for differing subgroup sizes: AVERAGEAVG_w = Σ n_i m_i / Σ n_i, where n_i is the size of subgroup i. The weighted form equals the overall mean of the pooled data.

Example. Suppose Group A has mean 4 with 3 observations and Group B has mean 9 with 2 observations. The unweighted AVERAGEAVG is (4+9)/2 = 6.5. The pooled (weighted) mean is (3*4 + 2*9) / (3+2) = 30/5 = 6.

Relation to other summaries. AVERAGEAVG can approximate the overall mean when subgroups are equal in size; otherwise, it can misrepresent the combined distribution, particularly if within-group variance differs or outliers are present in specific groups.

Applications and limitations. The concept is used in simple meta-analytic pooling, educational reporting, and survey summarization where subgroup means are readily available. Its main limitation is that it ignores within-group dispersion and distribution shape, so it may obscure variability present in the data. When subgroup sizes vary, the weighted variant provides a more accurate reflection of the total dataset.