Find the interquartile range and the semi-interquartile range of the following data:

42 51 53 53 59 61 75 100

mean=61.75=62
median=56
mode=53

interquartile range=87.5-52=35.5?

12

To find the interquartile range and the semi-interquartile range, you need to first calculate the first quartile (Q1) and the third quartile (Q3).

1. Arrange the data in ascending order:
42, 51, 53, 53, 59, 61, 75, 100.

2. Find the median (Q2), which is the middle value of the dataset. In this case, the median is 56.

3. Find the first quartile (Q1), which is the median of the lower half of the dataset. In this case, the lower half of the dataset is 42, 51, and 53. The median of this subset is (51 + 53)/2 = 52.

4. Find the third quartile (Q3), which is the median of the upper half of the dataset. In this case, the upper half of the dataset is 59, 61, 75, and 100. The median of this subset is (61 + 75)/2 = 68.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 68 - 52 = 16.

6. Calculate the semi-interquartile range (Semi-IQR) by dividing the IQR by 2: 16 / 2 = 8.

Therefore, the interquartile range is 16 and the semi-interquartile range is 8.