Measures of central tendency basics – UGC NET Question

Statements A, B and E state standard facts about central tendency. A is correct because mean can lie left or right of the median in skewed distributions or coincide in symmetric cases. B is correct for perfectly symmetric unimodal distributions such as the normal distribution. E is correct since the median position splits an ordered data set into two halves with equal counts. C is false because mean and median need not always be equal, and D is false because mode may be non-unique or even absent, so A, B and E only is the correct combination.

Option A:
Option A is correct since it includes all and only the true statements: A about relative positions of mean and median, B about equality in symmetric unimodal distributions and E about the median’s partition property. It excludes C and D, both of which overstate what must always happen.

Option B:
Option B is incorrect because it adds C, which wrongly claims that median always equals mean for any data set. Including C introduces a false universal statement about equality of mean and median.

Option C:
Option C is wrong as it includes C again, making the set A, B, C, E contain one false member. A correct combination must consist entirely of true statements, so this option cannot be chosen.

Option D:
Option D is incorrect because it includes D, which asserts that the mode must always be unique. In reality, a distribution may be bimodal, multimodal or have no mode, so adding D makes this option incorrect.