Calculate the first, second, and third quartiles:

20,26,28,25,31,14,23,15,12,26,29,24,31,19,31,17,15,17,20,31,32,16,21,22,28

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http://www.mathsisfun.com/data/quartiles.html

To calculate the first, second, and third quartiles, you need to follow these steps:

Step 1: Sort the data in ascending order.
12, 14, 15, 15, 16, 17, 17, 19, 20, 20, 21, 22, 23, 24, 25, 26, 26, 28, 28, 29, 31, 31, 31, 32

Step 2: Calculate the median (second quartile).
Since there are 24 numbers, the median will be the average of the 12th and 13th terms: (22 + 23) / 2 = 22.5
So, the second quartile (Q2) is 22.5.

Step 3: Calculate the first quartile (Q1).
The first quartile divides the lower half of the data set. To find it, you need to locate the median (Q2) of the lower half of the sorted data.
The lower half of the data is: 12, 14, 15, 15, 16, 17, 17, 19, 20, 20
Since there are 10 numbers in the lower half, the median will be the average of the 5th and 6th terms: (16 + 17) / 2 = 16.5
So, the first quartile (Q1) is 16.5.

Step 4: Calculate the third quartile (Q3).
The third quartile divides the upper half of the data set. To find it, you need to locate the median (Q2) of the upper half of the sorted data.
The upper half of the data is: 23, 24, 25, 26, 26, 28, 28, 29, 31, 31, 31, 32
Since there are 12 numbers in the upper half, the median will be the average of the 6th and 7th terms: (26 + 28) / 2 = 27
So, the third quartile (Q3) is 27.

Therefore, the first quartile (Q1) is 16.5, the second quartile (Q2) is 22.5, and the third quartile (Q3) is 27.