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Find the upper quartile for the data set {7, 5, 10, 5, 5, 6, 3, 5, 5, 4, 3}.

a) 5
b) 6
c) 7
d) 10

1 Answer

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Final answer:

The third quartile, or upper quartile (Q3), for the data set is 6 after ordering the data and finding the median of the upper half.

Step-by-step explanation:

The student's question involves finding the upper quartile, or third quartile (Q3), for the given data set {7, 5, 10, 5, 5, 6, 3, 5, 5, 4, 3}. First, order the data set from least to greatest and find the median to split the data into two halves. The ordered data set looks like this: 3, 3, 4, 5, 5, 5, 5, 5, 6, 7, 10. The median is 5, which is also the second quartile (Q2). To find Q3, we only consider the upper half of the data set which, after removing the median value, is 5, 5, 6, 7, 10. We now find the median of this upper half which is 6. Therefore, the third quartile (Q3) for this data set is 6.

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