- CFA Exams
- CFA Exam: Level I 2021
- 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**

A sample of the salaries of 4 employees from a large company was taken. 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 gives the sum of 78 (squared deviations). Divide by m - 1 = 3 to get the variance.

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**User Contributed Comments**
18

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 |

2014 |
Thanks Jim |

bidisha |
wow thanks jim |

Shaan23 |
Stop using calculators...you dont understand anything and its fast without it...just find the average of the numbers 31+33+24+36/4 = 31 now just use each value and subtract the mean and square it -- Just use your head...for the first value 0 then second 2^2=4 then 7^2 =49 and 5^2 = 25....then 0 + 4 + 49 + 35 = 78 divide that by 3.... only section you need to ever use the calculator is time value calculations and stuff... |

Kennyk11 |
Man, need to be careful with that N - 1 denominator, always gets me.... :p |