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Answer :
The 10th, 50th, and 100th percentiles for the given set of observations \(32, 49, 23, 29, 118\) are \(23, 32, 118\) respectively.
To calculate percentiles, we first need to arrange the observations in ascending order: \(23, 29, 32, 49, 118\).
The 10th percentile represents the value below which 10% of the data falls. In this case, 10% of 5 observations is \(0.1 \times 5 = 0.5\), which means we need to find the value at the 0.5th position. The 0.5th position falls between the first and second observations, which are 23 and 29. To find the value at the 0.5th position, we can take the average of these two numbers: \((23 + 29)/2 = 26\). Therefore, the 10th percentile is 23.
The 50th percentile represents the median or the middle value of the data. Since we have an odd number of observations, the middle value is the third observation, which is 32. Therefore, the 50th percentile is 32.
The 100th percentile represents the maximum value in the data set. In this case, the maximum value is 118. Therefore, the 100th percentile is 118.
In summary, the 10th, 50th, and 100th percentiles for the given set of observations are 23, 32, and 118 respectively.
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