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Find the third quartile Q₃ of the kt of 24 sorted values shown below

Thus the third quartile Q₃ is ______
(Type an integer as a decimal)

1 Answer

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Final answer:

The third quartile (Q3) is found by determining the middle value or the average of the middle two values of the upper half of the dataset, which consists of the values greater than the median.

Step-by-step explanation:

To find the third quartile (Q3), also known as the 75th percentile, we must locate the value above which the top 25% of the data lies. If we have an even number of data values, Q3 is the median of the upper half of the dataset; if we have an odd number of data values after excluding the median, Q3 is the middle value of the upper half.

In a dataset with 24 sorted values and a given median of 7 (Q2), Q3 will be the median of the 12 values that are greater than the median. Since there are 12 values in the upper half, we determine Q3 by taking the average of the 6th and 7th values from this subset. If the 6th and 7th values are, for example, 9 and 10, then Q3 is (9+10)/2 = 9.5. However, in this question, we are asked to provide an integer value, so we would round if necessary.

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