78, 69, 45, 89, 74, 37, 99, 77, 100, 82. What is the interquartile range of these scores?

Please arrange these scores in numerical order.

After you post them, I'll help you solve the rest of the problem.

37, 45, 69, 74, 77, 78, 82, 89, 99, 100

To find the interquartile range (IQR) of a set of scores, you need to calculate the first quartile (Q1) and the third quartile (Q3).

Here's how you can do it:

1. Arrange the scores in ascending order: 37, 45, 69, 74, 77, 78, 82, 89, 99, 100.

2. Determine the median, which is the middle value of the dataset. In this case, the median is between the 5th and 6th scores: (77 + 78) / 2 = 77.5. We can consider this the 50th percentile.

3. Calculate Q1, which is the 25th percentile. To do this, find the median of the lower half of the dataset. In this case, the lower half is: 37, 45, 69, and 74. The median of this lower half is between the 2nd and 3rd scores: (45 + 69) / 2 = 57. Q1 is 57.

4. Calculate Q3, which is the 75th percentile. Find the median of the upper half of the dataset. In this case, the upper half is: 78, 82, 89, 99, and 100. The median of this upper half is between the 3rd and 4th scores: (82 + 89) / 2 = 85.5. Q3 is 85.5.

5. Finally, compute the IQR by taking the difference between Q3 and Q1: IQR = Q3 - Q1 = 85.5 - 57 = 28.5.

Therefore, the interquartile range (IQR) of the given scores is 28.5.