- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 1. Rates and Returns
- Subject 2. Rates of Return

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**CFA Practice Question**

If one or more numbers in a data set are negative, which of the following is not always defined?

B. harmonic mean

C. geometric mean

A. holding period return

B. harmonic mean

C. geometric mean

Correct Answer: C

The geometric mean involves taking mathematical roots. These operations are not always defined to give real numbers when you are dealing with negative numbers.

A set of data can have more than one mode, or even no mode.

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**User Contributed Comments**
4

User |
Comment |
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ReaClute |
Ok, but the mode may also not be defined, and that could be true for a dataset of all positive numbers too - true? (The mode would not be defined, for instance, if there was only one incidence of each number in the dataset.) |

tracy |
The question asked which one is not ALWAYS defined. A geometric mean cannot be computed in this case but the mode may be, right? So C is the correct answer. |

Ioannis |
A single mode would not be defined, but multiple ones would, i.e. the distribution would be multimodal. |

tschorsch |
"not always defined" is NOT "never defined" it means "sometimes defined" C is the answer because sometimes you cannot calculate the root of a negative number resulting in real number value |