- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 4. Measures of Center Tendency

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**CFA Practice Question**

An employee had the following percentage increases in salary over the last 5 years: 4%, 7%, 10%, 15%, 12%. The geometric mean of his salary increases equals ______.

B. 8.72%

C. 9.53%

A. 9.22%

B. 8.72%

C. 9.53%

Correct Answer: B

The straight geometric mean of the increases is (0.04*0.07*0.1*0.15*0.12)

^{(1/5)}= 8.72%.Note that this is different from the geometric rate of change, which, in this case, would be (1.04*1.07*1.1*1.15*1.12)

^{(1/5)}- 1 = 9.53%. You should be very careful here, since the textbook is quite ambiguous on this point. Note that the geometric mean may not be defined if some of the salary changes are negative.###
**User Contributed Comments**
17

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

cbb1 |
Normally geometric rate of change is computed by adding one; geometric mean is using actually numbers -- results in a different answer. |

RichWang |
What is the finacial meaning for this straight geometric mean? |

surob |
Be careful. Tricky, but good one. |

Mariecfa |
Straight geometric exist, only if the product under the radical sign is non-negative. Impose the restriction that all the observations are greater than or equal to zero. |

TammTamm |
Ok, this upsets me because I was very excited when I calculated the geometric mean and subtracted one but now I know there are two formulas to remember. :( |

jpducros |
I don't really see in which context this 8,72 % would be useful. Do negotiate a salary increase, I believe the employee would either use an arithmetic mean, either the 9,53% mentioned above. Isn'nt it? |

DonAnd |
I am with you on that note Tamm Tamm! |

magus |
Can anyone advise on how to calculate the geometric mean with the BA II Plus calculator? |

2014 |
There is nothing to remember when compounded performance asked we are using 1.04 ..... rest is same |

johntan1979 |
Sigh, got this wrong, but the explanation makes a lot of sense. You add 1, root and subtract 1 only when you are calculating the compounding effect, i.e. annual rate of return. No point doing that in this question, since the compounding effect of salary increase is meaningless. |

davcer |
you can always compute a geometric rate of change but not a geometric mean with negative numbers. |

jdkuepper |
As a reminder, on the BAII+, you input the multiplied numbers, press y^x, input the nth root, press 1/x, then press = for the answer. |

Yrazzaq88 |
JUST DO THIS ON YOUR BA PLUS II CALCULATOR: 1 ) MULTIPLY ALL THE NUMBERS 2 ) PRESS Y^x , 5. 3) PRESS 1/x 4) Press = 5) Multiply by 100 |

Rachelle3 |
in geometric mean if it gives you 5 numbers you times each one then press = after this you know you had to times 5 numbers so sq root the answer of that long multiplication by 5. if there were 17 numbers given then times them all then sq root it by 17! |

linzlinked |
So confused! When to use the numbers themselves, and when to add 1, again? Is it if there is no negative number, we should use the numbers themselves? |

rehaanj |
On the TI BA II Plus, this is what I did, and it worked just fine: 1) (0.04*0.07*0.10*0.15*0.12) = .00000504 2) PRESS y^x, ".20" (since 1/5 = 0.20, so this gives us .00000504^0.20 = 0.08719) 3.) Multiply 0.08719 by 100 to get 8.719 |

Sm7272 |
What is the conceptual meaning of geometric rate of change? There is no such term in the CFA book. |