- 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**

A sample was taken of the salaries of 4 employees from a large company. The following are their salaries (in thousands of dollars) for this year: 33, 31, 24, 36. The variance of their salaries is ______.

Correct Answer: 26

The mean of these numbers is 31 and the four deviations from the mean are 2, 0, -7, and 5. Squaring these deviations and adding them equals 78 (the sum of the squared deviations). Divide by m - 1 = 3 to get the variance.

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**User Contributed Comments**
16

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

kaliokale |
This is the sample variance not the population variance |

willeen |
what number is m in the explanation above? thanks! F |

Cooltallgal |
m is 4 in this case as it stands for the 4 employee's salaries. |

bwbarksdale |
remember that the sample variance divides by "1" less than the population variance in order to achieve an "unbiased" measure of dispersion. |

janetse |
What are the steps in BAII? |

JimM |
Steps in BAII: 1) 2nd - DATA 2) enter the four data points as X values, leaving Y values alone (defaults to 1.0000) 3) 2nd - STAT 4) down arrow to read Sx (5.0990) 5) Variance is square of Sx, so hit x^2 button (26.0000) |

albert2008 |
Thanks for the calc instructions!!! |

JanLani |
Yeah, the calculator trick is greatly appreciated. |

morek |
Anyone know instructions for HP12C? Thanks. |

czim |
HP12c ; enter the data values using E+ in the stats function. Then key g s Enter to give you the standard deviation of the sample. simply square this to get sample variance. |

tschorsch |
for HP12c f Σ i.e. f SST clears stat data 33 Σ+ 31 Σ+ 24 Σ+ 36 Σ+ g s i.e g . g x² or enter x |

DonAnd |
Thanks for the steps using BA11. These are one set of formulas that I made sure that I knew well so I just use the formula but the calculator steps will definitely save me some time. |

harpalani |
Guys, can someone please explain the logic of reducing 1 from number of samples for calculating sample variance. How does the sample variance become biased when sample size is not reduced by 1? |

ThomasDess |
Steps in BAII' - cf JimM post 3) 2nd - Stat 3') 2nd - SET - press repeatedley until the CALCULATION METHOD you want is displayed; for one-variable data set 1-V; !! - for this case we would find the same results for Sx for Lin and Exp methods but not for Ln and PWR 4) down arrow to read Sx etc |

thekobe |
very important to put attention at the word "sample" |

2014 |
Thanks Jim |