- 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**

Increasing the frequencies in the tails of a distribution will ______.

A. reduce the standard deviation

B. increase the standard deviation

C. not affect the standard deviation as long as the increases are balanced on each side of the mean

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**User Contributed Comments**
7

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

joe3 |
Does the "Increasing the frequencies in the tails of a distribution" means the tail will be more peaked? Because more data accumulate around the mean, should the standard deviation be reduced? |

chamad |
What I understood is that you have more data in your sample, then more mean deviations then increasing std deviation. Please correct me If I'm wrong! |

micheleus |
more data in your sample decrease your mean deviation because your sample reach to your population. |

StanleyMo |
can i explain in this way, given number 1 to 10, the average 5, if let say i add more 10 into this series of numbers, then the SD is increasing? |

sheenalim |
Stanley, ur correct. i think the question meant shifting the frequencies of the data to the tail without increasing the sample itself. meaning there is more data around the tail than being centred around the mean. if u try it on a simple eg: 1) 3,5,7,9,11 with mean=7 s = square root of 10 now if add frequency to the tail, 2) 3,3,7,11,11 s = square root of 16 which is higher than the first eg. |

Saxonomy |
Increasing the frequencies in the tails (whether changing the sample size or not) will increase the standard deviation. A greater presence in the extremes enhances the chances that a selected value will fall in that area, hereby increasing the SD. More chance to be far from the mean definitely means a higher deviation "rate" for the sample size. If my English doesn't make sense...hey, it's past midnight. Darn CFA. |

AnalystBklyn |
The tails will get "fatter" and the frequency at the mean will get "lower". Overall your graph would like flatter rather than more peaked, which all implies a lower standard deviation! |