Quartiles

Question

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%.

fp92 · Answer

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 · Answer

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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