Posted by **carmen** on Sunday, April 29, 2007 at 12:13am.

Please help me to find the first and third quartiles, Q1 and Q3, of the following set of numbers.13, 7, 15, 13, 13, 12, 9, 11, 19, 9

Qrrange the numbers in ascending order, like this:

7, 9, 9, 11, 12, 13, 13, 13, 15, 19

Now divide then into the lowest quartile (Q1), second quartile, third quarter (Q3), and largest quartile.

Since there are ten numbers, there will be 2 1/2 numbers per quartile. The third largest number (9), be part of both Q1 and Q2, for example.

The third quartile will be the number 13 only.

The first quartile Q1 (or lowest quartile) is the median (middle) of the lowest half of the numbers. The third quartile Q3 is the median (middle) of the upper half of the numbers. First order the numbers from lowest to highest:

7, 9, 9, 11, 12, 13, 13, 13, 15, 19

The median of this data set is the middle value of all the numbers. The middle is between 12 and 13 (for an even set of numbers), which would be 12.5 in this case. (For an even set of numbers, you take the average of the two middle numbers. For an odd set of numbers, the median is the middle number.)

Pick the middle number of the five lowest numbers for Q1. Pick the middle of the 5 highest numbers for Q3.

Hopefully, this will help with other problems of this type.

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