Q. The value of which of the following will not change if a constant number is added to all the scores of a series?

The correct answer is: (B) Standard deviation

Explanation:

1. Median: The median is the middle value of a data set when arranged in order. If a constant number is added to all the scores, the position of the middle value remains the same, but the value itself will increase by the constant. Hence, the median changes.

2. Standard deviation: The standard deviation measures the spread or dispersion of the data around the mean. Adding a constant to all the scores shifts the entire data set by that constant, but it does not affect the spread of the data. Therefore, the standard deviation remains unchanged.

3. Mean: The mean is the average of all the scores. If a constant is added to all the scores, the total sum of the scores increases by that constant multiplied by the number of scores, which in turn increases the mean. Hence, the mean changes.

4. Mode: The mode is the most frequently occurring value in a data set. If a constant is added to all the scores, the most frequent value will also increase by that constant. Hence, the mode changes.

Thus, the standard deviation is the only measure that does not change when a constant is added to all the scores in a series.