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Answer :
The 40th percentile of the given data set is calculated to be 32.76.
To calculate the 40th percentile of the given data set, we first need to arrange the data in ascending order:
1.6, 18.5, 28.3, 29.6, 30.2, 31.4, 34.8, 36.6, 37.4, 40.7, 42.6, 43.3, 59.2, 59.5, 63
The formula for finding the percentile position is: Percentile Position = (Percentile/100) * (N + 1), where N is the number of data points.
In this case, for the 40th percentile:
Percentile Position = (40/100) * (15 + 1) = 0.40 * 16 = 6.4
This means the 40th percentile is between the 6th and 7th data points. We find the exact value by linear interpolation:
6th data point: 31.4
7th data point: 34.8
The 40th Percentile is calculated as follows:
P40 = 31.4 + 0.4 * (34.8 - 31.4)
= 31.4 + 0.4 * 3.4
= 31.4 + 1.36
= 32.76
Therefore, the 40th percentile is 32.76.
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