Can someone help me understand the explanation underlying the 60% figure? I can''t figure out how they got this from the answer key. My understanding is What are the median and the third quintile of the following data points, respectively?9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%A)13.1%; 13.7%.B)13.1%; 13.6%.C)12.8%; 13.6%.ExplanationThe median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7th term.The formula for determining quantiles is: Ly = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8th and 9th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 – 0.136) = 0.1372, or 13.7%.

Quintiles divide data into 5 equal parts, i.e. fifths. So 3rd quintile splits the data set into the lower 60% of values and the upper 40% of values. That's where 60 comes from.

A CFA Level 1 Discussion About Quartiles

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This topic has 3 replies, 4 voices, and was last updated 3w by norrisdietrich.

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- pcunniff
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  - CFA Level 1
  26 Nov 2020 at 10:50 pm
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  Can someone help me understand the explanation underlying the 60% figure? I can”t figure out how they got this from the answer key. My understanding is
  
  What are the median and the third quintile of the following data points, respectively?
  
  9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%
  
  A)
  
  13.1%; 13.7%.
  
  B)
  
  13.1%; 13.6%.
  
  C)
  
  12.8%; 13.6%.
  
  Explanation
  
  The median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7th term.
  
  The formula for determining quantiles is: Ly = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8th and 9th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 – 0.136) = 0.1372, or 13.7%.
- fp92
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  - CFA Level 1
  28 Nov 2020 at 7:00 am
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  Quintiles divide data into 5 equal parts, i.e. fifths. So 3rd quintile splits the data set into the lower 60% of values and the upper 40% of values. That’s where 60 comes from.
- norrisdietrich
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  - FRM Part 1
  29 Mar 2024 at 7:43 am
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  - Formula: They use the formula Ly = (n + 1)(y) / (100) to determine the position of the yth quintile (where y represents the percentile, in this case 60 for the third quintile).
  - Calculation: Plugging in the values (n = 13 for the number of data points and y = 60 for the percentile), they get: L(60) = (14)(60) / (100) = 8.4.
  - Interpretation: This value (8.4) doesn’t directly correspond to a specific data point because it falls between the 8th and 9th positions (13.6% and 13.9%) in the ordered data set.
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