Calculate Upper Quaritle : 98,89, 70,72.75, 60, 62
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Upper Quartile Definition and Formula
The upper quartile is the median of the upper half of a data set. This is located by dividing the data set with the median and then dividing the upper half that remains with the median again, this median of the upper half being the upper quartile.
The formula for the upper quartile is given as:
For ease of writing, the upper quartile will be noted as Q3, also called the third quartile. This formula does not give the value of Q3, rather the term number that will be Q3. N represents the number of elements in the data set. For example, if there are 9 elements in the data set, n = 9. To use the formula (n + 1) will equal 10, and then this is multiplied by 3/4 to obtain 7.5. This means the 7.5th term will be Q3, which will be the average of the 7th and 8th terms.
For a data set with 11 elements, then n = 11. To use the formula, (n + 1) will equal 12, and this will be multiplied by 3/4. This gives us 9, which means the 9th term in the data set will be Q3.
Sometimes, the formula will result in an answer that is not a whole number and does not end in .5. If this is the case, then subtract the answer by .25 and then follow the earlier provided rules. An example would be a set with 10 elements. Using the formula results in an answer of 8.25. This should be subtracted by .25 to yield 8, meaning the 8th term would be the upper quartile. A similar example would be a data set with 4 items. Using the formula would give an answer of 3.75, which should be subtracted by a .25 to yield an answer of 3.5. The upper quartile will be the average of the 3rd and 4th terms.