- 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**

A survey of the number of claimed dependents on 12 randomly selected tax returns yielded the following: 1, 4, 5, 6, 1, 3, 3, 2, 5, 6, 4, 3. Find the first quartile, median, third quartile, and interquartile range for this data.

B. 2.5, 3.5, 5.0, 2.5

C. 5.5, 3.0, 5.0, 0.5

A. 2.5, 3.0, 5.5, 3.0

B. 2.5, 3.5, 5.0, 2.5

C. 5.5, 3.0, 5.0, 0.5

Correct Answer: B

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**User Contributed Comments**
28

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

geet |
Everything I've readin this has said to linearly interpolate it if the number of obs. is even. |

vt96 |
this question is a trick to do alot of work. i've noticed that B has different median then the rest. and getting the median is the fastest computation. |

yanpz |
What is interquartile? |

mtcfa |
Interquartile = Q3 - Q1; 5 - 2.5 = 2.5. |

catburglar |
I come up with 2.25 for the 1st quartile. and 2.75 for the inter. what is the descrepancy |

AyshaAli |
i did not get how they got the answer? could any one help? |

Damy4real |
who can throw more light on this, pls? |

BayAreaPablo |
First you might find it easy to rearrange the numbers to this: 1,1,2,3,3,3,4,4,5,5,6,6 To calculate first quartile: take first 6 numbers: 1,1,2,3,3,3 and then take median. To calculate median: rearrange the numbers to: 1,1,2,3,3,3,4,4,5,5,6,6 Therefore the middle number (median) is 3.5 To calculate 3rd Quartile: Take last 6 numbers: 4,4,5,5,6,6 Then take middle number: 5 To calculate Interquartile: Please refer to mtcfa post Cheers |

surob |
Indeed, 1st quartile should be 2.25, not 2.50. Any comments on that? |

Indira |
1st quartile is 2.50: first six numbers in the data set (rearranged in ascending order) are 1,1,2,3,3,3 -> take the median (2+3)/2=2.5 |

thekapila |
calculate median and there is only 1 choice !!! |

soarer1 |
Remember to calculate the easiest one (the median) first. oh yea! |

jainrajeshv |
I am agreed with surob Q1 should be 2.25. If not then tell me why? |

TammTamm |
Thanks bayareapablo. It makes sense now. |

Meka76 |
To work it out this is what I did: Q1 = (n+1)*y/100 = (12+1)*.25=3.25; the 3rd number in the rearranged data is 2 and the 4th number is 3; (2+3)/2 = 2.5 You should know how to work out the median... Q3= 13*.75=9.75; the 9th number is 5 and the 10th number is also 5 in the sequence, so the average is 5. mtcfa has already explained interquartile range. Indira explained gave an even simpler way of working it out, but to save on time if the median is distinctly different than the other answer choices, then there lies your answer! |

surjoy |
there is discrepancy between how the first quartile is calculated here and how it is defined in CFA book. Surob is correct. Q1 is 2.25 - location of quartile is 3.25 i.e .25 distance between 3rd and 4th value and not halfway as described by Mekha76. Hence 2 + (3-2)*0.25 = 2.25 |

wulin |
You guys are making this way too hard. 1) Rearrange this into: 112|333|445|566 2)Q1 is between 3rd and 4th, which is 2.5. Q2,aka Median, is between 6th and 7th, which is 3.5 Q3 is between 9th and 10th, which is 5. 3)InterQ = Q3-Q1 = 2.5 |

panvino |
I agree with surjoy - there is a discrepancy. the textbook would give 2.25. |

meghanchloe |
I can follow meka76 |

peteSP |
thanks wulin! |

laotching |
wulin and meka76 have described a different method from the book's method. they are merely taking the midpoint of the two numbers the quartile lies between. the book advocates finding a point that may not be the midpoint. the CFA-correct methodology would be 12 (observations) + 1, divided by 4 (quartiles) = 3.25. so the first quartile is at 3.25, the second at 6.5, and the third at 9.75. the 3.25th number is 25% of the way between the 3rd and the 4th numbers => 2.25. the 6.5th number is 50% of the way between the 6th and 7th numbesr => 3.5. the 9.75th number is 75% of the way between the 9th and 10th numbers => 5. |

loisliu88 |
agree with laotching. | got the same answer |

safash |
wulin u the man |

johntan1979 |
wulin and meka76 are right, answer is B. No discrepancy. Good luck to whoever thinks otherwise. |

alester83 |
if you follow the CFA books (i checked this like 5 times)using the formula you get 3.25. that means the first quartile is in between the 3rd and 4th observation. According to that text you would take 25% of the difference between the 3rd and 4th observation =2.25. you cannot simply group them in the other examples otherwise you are taking 50% of the difference between the 3rd and 4th observation |

ewchen |
3.25 is correct according to the calculation formula in the CFA book. I agree to loatching and alester83 |

2014 |
As per text book: n + 1 * .25, = 12+1 = 13*.25 = 3.25 Now textbook says to look at observation and compare this result. So, its between 2-3, Now it is 25% of distance between 2 and 3 (3-2) = 1 1 * .25 = .25 Now add this to 2, 2.25 (so we have reached 25% of the distance from 2 by adding the result) 1 |

abs013 |
Find the median first |