The teacher had marks for 50 students in his class. He computed their mean and standard deviation. Considering that the evaluation was too strict, he gave five grace marks to each student. This would:
(a) Increase mean by five
(b) Alter standard deviation in an unpredicted way
(c) Change the rank order of the students
(d) Change the skewness of the distribution
Choose the correct option:

Correct option is A

When a constant value (5 marks) is added to every score in a distribution, it results in a linear transformation that affects only measures of central tendency but not measures of variability or distribution shape. Specifically, (a) the mean increases by exactly 5, as each score contributes equally to the sum. However, (b) standard deviation remains unchanged because it measures spread or dispersion, which is unaffected by uniform shifts; (c) rank order is preserved since all students receive the same addition; and (d) skewness remains constant as the distribution's shape is unchanged by parallel translation. This follows fundamental psychometric principles of score transformation, making option 1 the only correct statement.

Information Booster :
● Linear transformation rule: Adding a constant c to all scores: New Mean = Old Mean + c; Standard Deviation remains unchanged
● Why SD is unaffected: SD measures deviation from mean; when all scores and mean shift equally, relative distances remain constant
● Rank preservation: Adding the same value to all scores maintains their ordinal relationships; if X > Y before, X + c > Y + c after
● Skewness invariance: Distribution shape (symmetry/asymmetry) is unchanged by location shifts; only spread changes (scaling) affect skewness
● Contrast with multiplication: Multiplying by constant changes both mean and SD; SD new = SD old × |constant|