If the standard deviation is 10 and each value is multiplied by 5, what is the new standard deviation?

To understand how the standard deviation changes when each value in a data set is multiplied by a constant, it's important to recognize that the standard deviation is affected proportionally by such operations.

In this scenario, the original standard deviation is 10. When each value is multiplied by a factor of 5, the new standard deviation is calculated by multiplying the original standard deviation by the same factor. Thus, the new standard deviation becomes:

New Standard Deviation = Original Standard Deviation × Multiplicative Factor

New Standard Deviation = 10 × 5 = 50

Therefore, when each value is multiplied by 5, the standard deviation also increases by the same factor of 5, resulting in a new standard deviation of 50. This understanding is fundamental in statistics as it illustrates how variability in data scales with linear transformations.