Measures of Variation Practice

Question

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Question
Consider the following dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25. What is the third quartile’s value? Round to the nearest tenth if necessary.(1 point)

Answer 1

To find the third quartile, first arrange the dataset in ascending order: 18, 20, 22, 22, 24, 25, 29, 30, 31.

Next, calculate the position of the third quartile using the formula: Q3 = (3/4)(n+1). In this case, n=9 because there are 9 data points.

Q3 = (3/4)(9+1)
Q3 = (3/4)(10)
Q3 = 7.5

Since 7.5 is between the 7th and 8th data points, we take the average of those two values:
Q3 = (25 + 29) / 2
Q3 = 27

Therefore, the third quartile’s value is 27.