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

Question

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

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Solution

(a) To find the low, Q1, median, Q3, and high, we first need to organize the data in ascending order, which is already done: 6, 9, 9, 10, 11, 11, 12, 13, 14.

  • The low is the smallest number in the data set, which is 6.
  • The high is the largest number in the data set, which is 14.
  • The median is the middle number when the data set is listed in ascending order. Since we have 9 numbers, the median is the 5th number, which is 11.
  • Q1 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 9 and 9, which is 9.
  • Q3 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 12 and 13, which is 12.5.

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

(b) The interquartile range (IQR) is Q3 - Q1, which is 12.5 - 9 = 3.5.

This problem has been solved

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

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