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6   9   9   10   11   11   12   13   14(a) Find the low, Q1, median, Q3, and high.

Question

6   9   9   10   11   11   12   13   14(a) Find the low, Q1, median, Q3, and high.

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Solution

To find the low, Q1, median, Q3, and high of the given data set, follow these steps:

  1. Arrange the data in ascending order: 6, 9, 9, 10, 11, 11, 12, 13, 14

  2. Identify the low (minimum) and high (maximum) values:

    • Low = 6
    • High = 14

  3. Find the median (Q2), which is the middle value. Since there are 9 data points, the median is the 5th value:

    • Median = 11

  4. Find Q1, which is the median of the lower half of the data (not including the median if the number of data points is odd). The lower half of the data is 6, 9, 9, 10, so Q1 is the average of the 2nd and 3rd values:

    • Q1 = (9 + 9) / 2 = 9

  5. Find Q3, which is the median of the upper half of the data (not including the median if the number of data points is odd). The upper half of the data is 11, 12, 13, 14, so Q3 is the average of the 2nd and 3rd values:

    • Q3 = (12 + 13) / 2 = 12.5

So, the low is 6, Q1 is 9, the median is 11, Q3 is 12.5, and the high is 14.

This problem has been solved

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