Math

QuestionFind the 64th percentile of a sorted data set with n=117n=117. Calculate P64=P_{64}=

Studdy Solution

STEP 1

Assumptions1. The data set is sorted in ascending order. . The total number of data points (n) is117.
3. The percentile we are looking for is the64th percentile.

STEP 2

First, we need to find the rank of the percentile. The rank is calculated by multiplying the total number of data points by the percentile (in decimal form) and then rounding up to the nearest whole number if the result is not a whole number.
Rank=ntimesPercentileRank = n \\times Percentile

STEP 3

Now, plug in the given values for n and the percentile to calculate the rank.
Rank=117times64%Rank =117 \\times64\%

STEP 4

Convert the percentage to a decimal value.
64%=0.6464\% =0.64Rank=117times0.64Rank =117 \\times0.64

STEP 5

Calculate the rank.
Rank=117times0.64=74.88Rank =117 \\times0.64 =74.88

STEP 6

Since the rank is not a whole number, we round up to the nearest whole number. This is because we can't have a rank that is a fraction of a data point.
Rank=75Rank =75

STEP 7

Now that we have the rank, we can find the64th percentile. This is the value at the75th position in the sorted data set.
64=Valueat75thposition_{64} = Value\, at\,75th\, position

STEP 8

Looking at the sorted data set, the value at the75th position is81.6.
64=81.6_{64} =81.6The64th percentile of the data set is81.6.

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