- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 6. Measures of Dispersion

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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. 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: Data Set 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**
9

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. |

long2012 |
The sample standard deviation of S is 2.74 and population of standard deviation is 2.58. |

chipster |
for once I answered correctly on just gut |

tichas |
though it needs calculation but the range is a good indicator as well |

cfastudypl |
Besides the range providing a good quick indication that data set S has a greater variability, if you look at the figures in data set T, you will see that there are repeated figures of the same values i.e 9 thrice and 11 twice indicating more constant values compare to data set S that has no repeated value and therefore is more volatile and hence the increased standard deviation. |