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In the data set below, what are the lower quartile, the median, and the upper quartile?
3345577889
lower quartile =

median =

upper quartile =

1 answer

To find the lower quartile, median, and upper quartile of the data set \(3345577889\), we can follow these steps:

  1. Arrange the data in ascending order (though it already appears to be sorted):

    • The data set: \(3, 3, 4, 5, 5, 7, 7, 8, 8, 9, 9\)

  2. Count the number of data points:

    • There are 11 data points.

  3. Calculate the median (the middle value):

    • Since there are 11 numbers, the median is the value at position \(\frac{n + 1}{2} = \frac{11 + 1}{2} = 6\). So, the median is the 6th number in the ordered list.
    • Median = \(7\) (the 6th number)

  4. Calculate the lower quartile (Q1):

    • Q1 is the median of the first half of the data (the lower 50%). The first half is \(3, 3, 4, 5, 5\) (the first five numbers).
    • Q1 is the median of this set. For 5 numbers, the median is the 3rd number, which is \(4\).

  5. Calculate the upper quartile (Q3):

    • Q3 is the median of the second half of the data (the upper 50%). The second half is \(7, 7, 8, 8, 9, 9\) (the last five numbers).
    • The upper half is \(7, 7, 8, 8, 9, 9\). Since there are 6 numbers, the median is calculated as the average of the 3rd and 4th numbers.
    • Q3 = \(\frac{8 + 8}{2} = 8\).

Now, we can summarize the results:

  • Lower quartile (Q1) = \(4\)
  • Median = \(7\)
  • Upper quartile (Q3) = \(8\)

Final Results:

  • Lower quartile = 4
  • Median = 7
  • Upper quartile = 8