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Find the 34th percentile, \( P_{34} \), from the following data:

11.5, 14.9, 15.1, 18, 24.6,
29.7, 33.7, 33.9, 34.7, 37.3,
38.1, 38.7, 38.8, 39.4, 41,
41.6, 41.8, 41.9, 43.4, 43.5,
44.9, 46, 48.2, 49, 49.5,
50

Answer :

Answer:

First, we need to sort the data in ascending order:

11.5 14.9 15.1 18 24.6 29.7 33.7 33.9 34.7 37.3 38.1 38.7 38.8 39.4 41 41.6 41.8 41.9 43.4 43.5 44.9 46 48.2 49 49.5 50

The total number of data points is 26.

To find the 34th percentile value, P34, is the value below which 34% of the observations fall. To find the exact location of this value, we multiply the total number of data points by 0.34:

26 * 0.34 = 8.84

Since the position we got isn't an integer, we need to interpolate between the closest positions. The 8th and 9th values in the sorted data set are 33.9 and 34.7, respectively.

We can use linear interpolation to find the exact value at position 8.84:

P34 = value at 8th position + ((value at 9th position - value at 8th position) * (0.84))

P34 = 33.9 + ((34.7 - 33.9) * 0.84)

P34 = 33.9 + (0.8 * 0.84)

P34 = 33.9 + 0.672

P34 = 34.572

So, the 34th percentile of the data set is approximately 34.572.

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Rewritten by : Jeany

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