In this case, the Interquartile Range (IQR) would be a better measure of variability to describe the spread of the dataset. This is because the IQR measures the range of the middle 50% of the data, which can give a better understanding of the overall variability while excluding potential outliers.
Calculating the IQR for this dataset:
1. Arrange the data in ascending order: 85, 88, 90, 90, 92, 92, 95, 96, 99
2. Find the first quartile (Q1) and the third quartile (Q3):
- Q1 = 90 (as it is the average of the two middle values: 88 and 90)
- Q3 = 95 (as it is the average of the two middle values: 95 and 96)
3. Calculate the IQR:
IQR = Q3 - Q1
= 95 - 90
= 5
The IQR for this dataset is 5, indicating that the middle 50% of the data falls within a range of 5 points. This gives a better understanding of the variability within the dataset while minimizing the impact of outliers.
Which measure of variability—range or IQR—best describes the spread of the dataset?
Social studies group project grades (out of 100 points) for Mr. Chang’s first period class
85 88 90 90 92 92 95 96 99
and can you explain
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