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Answer :
The calculated percentiles are as follows:
10th percentile: 21
50th percentile (Median): 40
100th percentile: 115
To calculate the 10th, 50th (also known as the median), and 100th percentiles from the given set of observations: 42, 29, 40, 21, 115, we need to sort the data in ascending order.
Ascending order: 21, 29, 40, 42, 115
Now we can calculate the desired percentiles:
10th percentile: The 10th percentile is the value below which 10% of the data falls. To calculate it, we multiply 10% (0.1) by the total number of observations (5) and round up to the nearest whole number. In this case, 10% * 5 = 0.5, which rounds up to 1. Therefore, the 10th percentile is the first observation in the sorted data, which is 21.
50th percentile (Median): The 50th percentile represents the middle value of the data set when arranged in ascending order. Since we have an odd number of observations (5), the median will be the middle value. In this case, the middle value is the third observation, which is 40.
100th percentile: The 100th percentile represents the maximum value in the data set. Since the maximum value in the given data set is 115, it is also the 100th percentile.
Therefore, the calculated percentiles are as follows:
10th percentile: 21
50th percentile (Median): 40
100th percentile: 115
Learn more about percentiles here:
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