Compute the third quartile for the following data. 10, 15, 17, 21, 25, 12, 16, 11, 13, 22
A)21.25
B)15.5
C)21.5
D)11.75

Question

Quizplus · Accepted Answer

To find the third quartile (Q3), first, we need to arrange the data in ascending order: 10, 11, 12, 13, 15, 16, 17, 21, 22, 25. The third quartile is the median of the upper half of the data. For 10 data points, the upper half after the median consists of the 6th to 10th data points: 16, 17, 21, 22, 25. The median of these is the average of the middle two numbers (since there are an even number of them), which is (21 + 22) / 2 = 21.5. However, given the choices, it seems there was a mistake in my calculation. Correctly, for a dataset of 10 numbers, Q3 is the 7.5th value. Interpolating between the 7th and 8th values (17 and 21), Q3 = 17 + 0.5*(21-17) = 17 + 2 = 19, which does not match any of the provided options directly. Re-evaluating the method for calculating Q3 in this context and considering the options, it appears there was a misunderstanding in the initial explanation. The correct approach to find Q3 involves dividing the dataset into quartiles and correctly interpreting the position and calculation method for Q3, which typically involves finding the median of the upper half of the data set. Given the discrepancy and re-evaluation, the correct answer based on standard calculation methods should indeed reflect the calculation of the third quartile for the given dataset, but none of the explanations align with the standard outcome of 21.5 or the recalculated value. Therefore, the initial selection was incorrect, and the correct explanation involves accurately sorting the data and calculating the third quartile based on the position in the sorted list, which typically would be between the 7th and 8th values for a 10-item dataset.

Compute the Third Quartile for the Following Data