- CFA Exams
- CFA Level I Exam
- Study Session 18. Portfolio Management (1)
- Reading 52. Portfolio Risk and Return: Part I
- Subject 2. Variance and Covariance of Returns

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**CFA Practice Question**

Listed below are two data sets: S and T. Which data set has the larger standard deviation? (Hint: you can answer this question by inspecting the two data sets. But if you are not sure after inspection, calculate the standard deviation.)

Data Set T: 8, 9, 9, 9, 10, 11, 11, 12

Data Set S: 1, 2, 3, 4, 5, 6, 7, 8, 9

Data Set T: 8, 9, 9, 9, 10, 11, 11, 12

Correct Answer: S

On inspection, data set S has the larger sample standard deviation. By calculation: S(S) = 2.58, S(T) = 1.27.

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**User Contributed Comments**
11

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

Lucho |
If it is a sample, you should use N instead of N-1 to calculate variance. It it is a population, then you should use N. |

namie |
good question. I guess it is a population variance that's why it uses only N, instead of N-1. In this question we are not trying the sample the data buy actually trying the calculate the sd directly. |

rfvo |
Here, i'll make it easy for ya....check the range |

dravinskis |
Agree with rfvo. |

AUAU |
I think no need to calculate. Just observe the deviation from mean. |

jayphx |
So when I use my hp12c: 1Σ+ 2Σ+ 3Σ+ 4Σ+ 5Σ+ 6Σ+ 7Σ+ 8Σ+ 9Σ+ the g and s I get 2.739. Can someone tell me what I'm doing wrong? |

johntan1979 |
Range means nothing, especially if both sets have the same range. The key to solving this question fast is by observing the difference between each number. Set S is consistently at least 1, while Set T has a few zeros. Logic and common sense will tell you that Set S definitely has the higher sd. |

jonan203 |
jayphx: you have to calculate the mean of the population and add it as the nth sigma before calculating the population standard deviation 1 <sigma> 2 <sigma> 3 <sigma> 4 <sigma> 5 <sigma> 6 <sigma> 7 <sigma> 8 <sigma> 9 <sigma> <g><mean><sigma> <g><s> = 2.58199 you have to do this because hp12c defaults to sample statistics. |

ascruggs92 |
Don't use a calculator for this. Standard Deviation is one of the measurement that establishes how much the observations in a population vary from the population mean. If the range of observations in the data set is bigger than that of another data set, it is said to have more variation. That can very literally be translation to "it has a larger variance", and because standard deviation is the square root of Variance, the standard deviation is higher as well. |

pigletin |
numbers in set s are more variant? hence the higher variance |

walterli |
No need to calculate... just compare the difference with the average for each number.... S has large difference than T |