Medelsumman

Medelsumman is a term used in statistics and data analysis to describe the sum of the arithmetic means of several groups or datasets. The Swedish word medel means mean, and summan means sum, so medelsumman is often understood as the unweighted sum of group means.

Definition and calculation: Given k groups with means m1, m2, ..., mk, the medelsumman is M = m1 + m2 + ... + mk. It is distinct from the overall mean across all observations, which is not the same as the unweighted sum of the group means unless the groups are equal in size.

Example: If three groups have means 4.0, 6.0 and 5.0, the medelsumman is 15.0.

Relation to other measures: A weighted variant exists when group i has size n_i; the overall mean is μ = (Σ n_i m_i)/(Σ n_i). The medelsumman remains the unweighted sum of the group means, and sometimes it is transformed into an unweighted average by dividing by the number of groups, producing (Σ m_i)/k.

Applications and limitations: The medelsumman is mainly used as a simple, intuitive summary in didactic contexts or when presenting unweighted summaries of separate groups. However, it can be misleading in comparisons across studies with different numbers of groups or varying sample sizes, and it should not replace standard measures such as the overall mean or weighted averages in rigorous analysis.

Status: The term medelsumman is not a standard term in most statistical texts; it appears mainly in informal Swedish-language discussions. When precision is needed, practitioners use explicit descriptions using means, totals, and weights.