Is it possible to find the interquartile range without plotting a cumulative frequency curve?
Answers:
All you need to do is sort your data numbers in order (or frequencies). Work out what nth value of the numbers is 1/4 of the subtotal of the data (i.e. 1/4 of the number of elements), the number in that position is your lower quartile.
Then do the same to find the 3/4 position and that's the upper quartile number. Take one from the other and you have the range.
if you have all the data points, then yes
Yes.
No.foolish mortal. Everyone knows THAT! Now, bow before the gods of frequency until they are appeased!
Yes.
In fact, one does not need to calculate or plot cumulative frequency. Quartile is about the number of data points leading up to 25%, 50%, and 75% of the data points in an ordered set of data. The value of the data point at the 50% mark is, by defintion, the median of a data set. This simply means that there half of the data points below that value and half of them above.
Check out:
"Quartile
From Wikipedia, the free encyclopedia
.
In descriptive statistics, a quartile is any of the three values which divide the sorted data set into four equal parts, so that each part represents 1/4th of the sample or population.
Thus:
first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile
second quartile (designated Q2) = median = cuts data set in half = 50th percentile
third quartile (designated Q3) = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile
The difference between the upper and lower quartiles is called the interquartile range.
Example 1:
Data Set: 6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36
Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
Q1 = 25.5
Q2 = 40
Q3 = 42.5
Example 2:
Ordered Data Set: 7, 15, 36, 39, 40, 41
Q1 = 15
Q2 = (39+36)/2 = 37.5
Q3 = 40" [See source.]
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