Average and weighted mean concepts – UGC NET Question

Statements A, B, C and E describe core properties of means. A gives the definition of arithmetic mean. B is true because the overall mean of two groups must fall between their group means, weighted by group sizes. C is correct in explaining that weighted averages give more influence to values with higher weights. E holds since adding a constant to all values shifts the mean by that constant. D is false because the mean need not be one of the data values, especially for continuous data. Hence A, B, C and E only are correct.

Option A:
Option A is incomplete because it leaves out E and therefore ignores the important transformation property showing how means shift under addition of a constant. It does not include all correct statements.

Option B:
Option B is wrong since it excludes C and includes only A, B and E, failing to mention the key feature of weighted averages, which are frequently tested in aptitude problems.

Option C:
Option C is correct because it collects all four true statements while excluding D, which wrongly asserts that the mean must be a data point. This combination matches the conceptual understanding required in NET statistics questions.

Option D:
Option D is incorrect as it omits A and does not include all four true statements together, so it cannot be the correct combination.