- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Statistical Measures of Asset Returns
- Subject 2. Measures of Dispersion

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**CFA Practice Question**

If a constant was to be added to a set of scores, the standard deviation would ______.

A. remain the same

B. increase by the square root of that constant

C. increase by the magnitude of that constant

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**User Contributed Comments**
5

User |
Comment |
---|---|

tenny45 |
if you review the notes you'll see that it mentions when a constant is added to standard deviation, st. dev stays the same; however, if the set of data is multiplied by a constant, then the st. dev also changes. |

ksnider |
can someone expand on why this is the case? |

Flavorman |
Use a numerical example and you will see that. |

Flavorman |
if we have: data 1,2,3 (here mean is 2) stdev=sqrt((1-2)^2+(2-2)^2+(3-2)^2)/(3-1)=sqrt(2)/2 Now if we add 1 to the data set above a we have the ff new data set 2,3,4 (here mean is 3) stdev=sqrt((2-3)^2+(3-3)^2+(4-3)^2)/2=sqrt(2)/2 |

mlaique |
Thank you Flavorman. I took it as the new data would have been: 1,2,3 and 4. |