- 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

###
**CFA Practice Question**

You receive a fax with 6 bids (in millions of dollars): 2.2, 1.3, 1.9, 1.2, 2.4 and x, where x is a number that is too blurry to read. Without knowing what x is, the median ______.

B. must be between 1.3 and 2.2

C. could be any number between 1.2 and 2.4

A. is 1.9

B. must be between 1.3 and 2.2

C. could be any number between 1.2 and 2.4

Correct Answer: B

The median is the average of the 3rd and 4th smallest observations. The 3rd smallest must be at least 1.3. It will be 1.3 when x <= 1.3, or else it will be larger. It can't possibly be smaller than 1.3. Similarly, the 4th smallest observation cannot exceed 2.2.

###
**User Contributed Comments**
8

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

limpus |
It will in fact be between 1.6 and 2.05 but B is still correct. |

aggabad |
How was that calculated? |

patsy |
no so sure how you came up with that limpus! |

julescruis |
good question |

tobikemper |
(1.3 + 1.9) / 2 = 1.6 (1.9 + 2.2) / 2 = 2.05 |

mordja |
no Tobikemper. Median in this instance will be the 6+1/2=3.5th result. What the answer is getting at is regardless of whether x is smaller than 1.2, the median will be larger than 1.3 (as this could only ever be the 3rd smallest number, with the median higher than it), and if x was larger than all numbers given the median would be smaller than 2.2 as it would only be the third largest number with the median smaller than it. |

johntan1979 |
There is no way you can calculate exactly. x can be any number less than 1.2, between 1.2 and 1.3, between 1.3 and 1.9, between 1.9 and 2.2, between 2.2 and 2.4 and larger than 2.4. But by using the supppositions above, you can safely infer that it will never be smaller than 1.3 or larger than 2.2 based on the number of observations, which is 6, meaning you hypothesize the x positions and see the average of the 3rd and 4th numbers. |

sshetty2 |
Once I focused on the number of values instead of the values themselves, it became clear. There are 5 numbers without x and 6 numbers with it. If there are 5 numbers then the median would be the third number, if there are 6 numbers then the median would be between the third and fourth number. This answer makes sense regardless of whether x is big or small. |