- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 5. Quartiles, Quintiles, Deciles, and Percentiles

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**CFA Practice Question**

The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2012. In each class interval, the left endpoint is included but not the right.

II. The first quartile must be at least 15 but no larger than 22.5.

Which statement is true?

I. The median rate must be less than 30.

II. The first quartile must be at least 15 but no larger than 22.5.

Correct Answer: II only

The first quartile is the average of the 6th and 7th smallest observations. From the histogram, we know the interval 7.5 <= rate < 15 contains one observation and the interval 15 <= rate < 22.5 contains 6 observations. Thus, there are 7 observations less than 22.5, which means that both the 6th and 7th smallest observations are less than 22.5 and their average, which is the first quartile, must be less than 22.5 as well.

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**User Contributed Comments**
7

User |
Comment |
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rinkoo |
can any one explain plzzzzzzzzz |

danfandango |
between 7.5 and 30 is 22.5, which means each interval is 7.5. The first quartile occurs between the sixth and seventh values, which can't possibly occur *based on the frequencies(there is only one value in the first interval and six in the second, the highest value in the second interval is the seventh)* until the second interval. So the value has to be between 15 and 22.5. Hope that helps. |

evelynham |
isn't the median greater than 30 since it's the 13th observation? |

tschorsch |
since the left endpoint is included, it could be 30 and thus not greater than 30 |

harpalani |
I'm lost!! Can anyone please explain how to locate quartiles in this histogram and how is the first quartile average of 6th adn 7th smallest observation? |

fsammari |
Can anyone explain |

robbiecow |
the 25th percentile = (n+1)*Q1, or (25+1)*.25 = 6.5. You are looking for the 6.5th observation. Since you are going from left to right it can't be that the 6.5th observation is in the first interval, because there is only 1 interval there; however, if you add the next 6 observations you are at 7. It must be so that the 1st quartile is between 15 (7.5 + 7.5) and 22.5 (7.5 + 7.5 + 7.5). The 7.5 is the length of each interval as pointed out by danfandango. |