Calculate the interquartile range for the following data set. 11,15,18,31,26,44,33,30,16,22,39 𝐼𝑄𝑅=

To calculate the interquartile range (IQR), follow these steps:

1. First, arrange the data in ascending order: 11, 15, 16, 18, 22, 26, 30, 31, 33, 39, 44.

2. Next, find the median (Q2) of the data set. Since there are 11 numbers, the median is the 6th number, which is 26.

3. Then, find the lower quartile (Q1), which is the median of the lower half of the data. The lower half is 11, 15, 16, 18, 22. The median of this set is 16.

4. Find the upper quartile (Q3), which is the median of the upper half of the data. The upper half is 30, 31, 33, 39, 44. The median of this set is 33.

5. Finally, subtract Q1 from Q3 to find the interquartile range. IQR = Q3 - Q1 = 33 - 16 = 17.

So, the interquartile range of the data set is 17.