Find the interquartile range of the data set {42, 49, 91, 42, 94, 73, 93, 67, 55, 54, 78, 82}.Group of answer choices5264035

To find the interquartile range (IQR) of a data set, follow these steps:

1. First, arrange the data set in ascending order: {42, 42, 49, 54, 55, 67, 73, 78, 82, 91, 93, 94}.

2. Next, find the median (Q2) of the data set. Since there are 12 numbers, the median is the average of the 6th and 7th numbers. So, (67 + 73) / 2 = 70.

3. Then, find the lower quartile (Q1), which is the median of the lower half of the data (not including Q2). The lower half is {42, 42, 49, 54, 55, 67}, so Q1 is the average of the 3rd and 4th numbers: (49 + 54) / 2 = 51.5.

4. Find the upper quartile (Q3), which is the median of the upper half of the data (not including Q2). The upper half is {73, 78, 82, 91, 93, 94}, so Q3 is the average of the 3rd and 4th numbers: (82 + 91) / 2 = 86.5.

5. Finally, subtract Q1 from Q3 to find the interquartile range: 86.5 - 51.5 = 35.

So, the interquartile range of the data set is 35.