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In the data set below, what is the upper quartile?

Ask by Fleming Joseph. in the United States
Mar 19,2025

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The upper quartile (Q3) of the data set is 9.

Solución

To find the upper quartile (Q3) of the given data set, we will follow these steps:
  1. Order the data set: The data set is already ordered: .
  2. Determine the position of Q3: The upper quartile (Q3) is the median of the upper half of the data. To find Q3, we first need to find the median of the entire data set.
  3. Calculate the median: Since there are 6 data points (an even number), the median is the average of the 3rd and 4th values.
    • The 3rd value is .
    • The 4th value is .
    Therefore, the median is calculated as:
  4. Identify the upper half of the data: The upper half of the data set consists of the values above the median. In this case, the upper half is:
  5. Calculate Q3: Since there are 3 values in the upper half, Q3 is the median of these values. The median of is simply .
Thus, the upper quartile (Q3) of the data set is .

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Mind Expander

To find the upper quartile, also known as the third quartile (Q3), you first need to arrange your data set in ascending order, which it already is: .
The upper quartile is the median of the upper half of the data set. Since there are six values, the upper half consists of the last three values: . The median of these three values is . Therefore, the upper quartile is .
A fun way to remember this is that the upper quartile is where three-quarters of the data lies below, so you can imagine it as the “VIP lounge” of your data set where the top scores hang out!

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