21,24,25,27,30,32,33,34,34,36,41,44
What is the IQR
The IQR (Interquartile Range) is a measure of statistical dispersion, or in other words, it is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. To find the IQR of the given dataset {21,24,25,27,30,32,33,34,34,36,41,44}, we first need to find Q1 and Q3.
To find Q1:
1. Arrange the data in ascending order: {21, 24, 25, 27, 30, 32, 33, 34, 34, 36, 41, 44}
2. Calculate the position of Q1: q = (n+1)/4
q = (12+1)/4 = 3.25
Since Q1 falls between the 3rd and 4th positions, we can find it by taking the average of the values at these positions:
Q1 = (24 + 25) / 2 = 24.5
To find Q3:
1. Calculate the position of Q3: q3 = 3(n+1)/4
q3 = 3(12+1)/4 = 9.75
Q3 falls between the 9th and 10th positions:
Q3 = (34 + 36) / 2 = 35
Now we can calculate the IQR:
IQR = Q3 - Q1
IQR = 35 - 24.5
IQR = 10.5
Therefore, the IQR of the given dataset is 10.5.