What is the value of 3 11
126.96.36.199.1 The determination of quartiles
The determination of quartiles (weighted):
- the values are ranked according to their size (our example: possession of books on ethnology)
e.g. 1, 2, 3, 3, 5, 7, 11, 16, 17, 17, 20, 22, 25, 48, 52, 56, 76, 89, 96, 115
There are 20 different entries, therefore n = 20.
- Calculation of the 1st quartile, i.e. the value which is greater than 25% and less than 75% of all values. Q1 is on the (n + 1) / 4. Job
In our example, this value is at the (n + 1) / 4 digit = 5.25, i.e. between the 5th value (= 5) and the 6th value (= 7). The fraction (0.25) indicates that in addition to the value of 5, ¼ of the distance between 5 and 6 is added. Q1 is therefore 5 + 0.25 * 2 = 5.5.
- Calculation of the 2nd quartile (is calculated like the median). This is between the 10th and 11th digits, so the value should be averaged (17 + 20) / 2 = 18.5
- Calculation of the 3rd quartile, i.e. the value which is greater than 75% and less than 25% of the sorted values. Q3 = 3 * (n + 1) / 4
In our example: Q3 = 3 * 21/5 = 15.75. Job. Q3 lies between the 15th value (= 52) and the 16th value (= 56). The fraction (0.75) indicates that ¾ of the distance between the 15th and the 16th value is added to the 15th value, therefore: Q3 = 52 + 0.75 * 4 = 55.
We can now state that people from the first or lowest quartile (quarter) have fewer than 5.5 books, while those from the top quartile have at least 55 books.
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