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Here is a data set (\(n = 117\)) that has been sorted:

51.7, 56.8, 65.3, 66.8, 67.3, 68.1, 68.1, 68.3, 68.6, 68.7, 69, 69, 69.6, 69.7, 69.9, 70.2, 70.8, 71.2, 71.3, 71.4, 71.7, 72.3, 72.6, 72.9, 73, 73.4, 74.3, 74.4, 74.6, 74.6, 75.2, 75.4, 75.5, 75.5, 75.7, 75.9, 76.3, 76.7, 76.8, 77.3, 77.4, 77.9, 78, 78.3, 78.3, 78.5, 78.7, 79, 79.4, 79.6, 79.6, 79.8, 80.2, 81.1, 82, 82.1, 82.2, 82.4, 82.9, 83.1, 83.3, 83.4, 83.4, 83.5, 83.6, 83.7, 83.7, 83.8, 84, 84.1, 84.5, 84.6, 84.9, 85.1, 85.3, 85.3, 85.5, 85.5, 86, 86.7, 86.9, 87, 87.6, 87.7, 87.7, 87.7, 87.8, 88.4, 88.5, 88.8, 89.1, 89.1, 89.1, 89.3, 89.5, 89.7, 90.4, 90.5, 90.6, 91, 91.1, 91.2, 91.9, 92, 92.2, 92.8, 92.9, 93.1, 93.9, 94.1, 95.1, 95.6, 96.9, 97.1, 97.3, 97.5, 100.1.

Find the 82nd percentile.

Answer :

The 82nd Percentile is 89.784

How to calculate percentile in statistics?

The formula n = (P/100) x N, where P is the percentile, N is the number of values in a data collection (ordered from least to largest), and n is the ordinal rank of a particular value, can be used to determine percentiles. In order to comprehend exam scores and biometric measurements, percentiles are routinely utilized.

The values' percentiles as determined by the formula are displayed below.

Percentile Value 0th = 51.7 5th = 68.1 10th = 69.36 15th = 71.24 20th = 72.92 25th = 74.6 30th = 75.86 45th = 80.38 60th = 84.34 65th = 85.38 70th = 87.12 75th = 88.4 80th = 89.4 85th = 90.84 90th = 92.44 95th = 95.2 100th = 100.1

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Rewritten by : Barada

The 82nd percentile of a data set can be found using the given percentile formula. By calculating the index for the 82nd percentile and rounding up, the corresponding data value at that index in the sorted data set will give the percentile value. However, the provided data snippets need to be properly ordered and combined into a single data set to find the correct percentile.

To find the 82nd percentile in a data set, you can use the formula:

i = (k/100) * (n + 1)

where i is the index of the percentile value, k is the percentile, and n is the total number of data points in the set.

For the 82nd percentile:

  • k = 82
  • n = 117

i = (82/100) * (117 + 1) = 96.56

Since the index i is not a whole number, we round up to the nearest whole number, which gives us the 97th position in the sorted data. Therefore, we look at the 97th data value in our sorted set to determine the 82nd percentile. If the dataset provided is the one we're supposed to use, we need to locate the 97th value in it. However, it's important to note that the provided data snippets are not one continuous data set, so we cannot directly calculate the 82nd percentile from them without combining them into a single, correctly ordered set.