33, 25, 42, 25, 31, 37, 46, 29, 38What is the third quartile (UQ) of the data?*1 point40374638
Question
33, 25, 42, 25, 31, 37, 46, 29, 38What is the third quartile (UQ) of the data?*1 point40374638
Solution
To find the third quartile (UQ) of the data, follow these steps:
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First, arrange the data in ascending order: 25, 25, 29, 31, 33, 37, 38, 42, 46.
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Then, find the median of the entire data set. In this case, the median is 33.
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The third quartile (UQ) is the median of the upper half of the data. The upper half of the data is: 37, 38, 42, 46.
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The median of this upper half is the average of 38 and 42, which is 40.
So, the third quartile (UQ) of the data is 40.
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Finally, find Q3.Recall that the third quartile, Q3, is the median of the upper half of the data. That is, the median of the data located above the Q2 position.Consider the ordered list of data values. The median, Q2, which has been determined, has been underlined for clarity.3, 6, 6, 7, 8, 8, 9, 10, 11There are nine values in the whole data set, but there are only values to the right of the underlined median. The third quartile, Q3, will be equal to the median of these values.Since the lower half of the data has an even number of data values, we will now use the rule to find the median of an even number of data values.median = sum of middle two values2The middle two values of the upper half are 9 and .Now, calculate the third quartile, Q3.Q3 = 9 + 2 = 2 =
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