The standard deviation of a set of 50 items is 6.5. If value of each item is increased by 5, then the standard deviation will be :

Question

Accepted Answer

The correct option is 2:

This question tests your understanding of the properties of standard deviation as a measure of dispersion. Standard deviation measures the spread or variability of the data points around the mean. The key principle here is the effect of a change of origin on measures of dispersion. When a constant value (in this case, 5) is added to every item in a dataset, it shifts the entire distribution along the number line, which changes the mean. However, the *spread* or *distance* of each data point relative to the new mean remains exactly the same as their distance from the original mean. Since standard deviation only measures the magnitude of the differences between the values and the mean, adding or subtracting a constant to all values does not change the standard deviation. Therefore, if the original standard deviation was 6.5, the new standard deviation will also be 6.5.

The incorrect option is 1:
Option 1 (11.5) is incorrect because it results from adding the constant value (5) to the original standard deviation (6.5). This mathematical operation is only applicable to measures of central tendency, like the mean, and not measures of dispersion.

The incorrect option is 3:
Option 3 (1.5) is incorrect. A decrease in standard deviation would only occur if the values were made less dispersed, for instance, by multiplying them by a fraction, not by adding a constant to each value. There is no logical or statistical rule that would lead to this result.

The incorrect option is 4:
Option 4 (32.5) is incorrect. This value is likely derived from multiplying the original standard deviation (6.5) by the constant added (5). This operation does not reflect the property of standard deviation under a change of origin and would only be relevant if the data were multiplied by the constant, not if the constant were added.