Find the range and interquartile range for the data set.{26, 48, 12, 32, 41, 35}

To find the range and interquartile range of a data set, follow these steps:

Step 1: Arrange the data in ascending order. The given data set is {26, 48, 12, 32, 41, 35}. When arranged in ascending order, it becomes {12, 26, 32, 35, 41, 48}.

Step 2: Find the range. The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 48 and the lowest value is 12. So, the range is 48 - 12 = 36.

Step 3: Find the interquartile range (IQR). The IQR is the range of the middle 50% of the data. To find the IQR, you first need to find the lower quartile (Q1) and the upper quartile (Q3).

Q1 is the median of the first half of the data. Since we have 6 data points, the first half is {12, 26, 32}. The median of this set is 26.

Q3 is the median of the second half of the data. The second half of the data is {35, 41, 48}. The median of this set is 41.

The IQR is then Q3 - Q1, which is 41 - 26 = 15.

So, the range of the data set is 36 and the interquartile range is 15.