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Up14
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%.
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Up4
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.
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Up3
- Formula: They use the formulaÂ
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 = 13Â for the number of data points andÂy = 60Â for the percentile), they get:ÂL(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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- Formula: They use the formulaÂ
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Up0
Great question! Just to add — when they ask for the 1st or 3rd quartile in the exam, they usually mean the 25th and 75th percentiles, respectively, using the inclusive method unless otherwise stated.
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