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
In this case, the range would best describe the spread of the dataset. The range is the difference between the highest and lowest values in the dataset, and it gives a direct measure of how spread out the data is. In this dataset, the range would be 99 - 85 = 14, indicating that the grades range from 85 to 99.
To determine which measure of variability best describes the spread of the dataset, we need to compare the range and interquartile range (IQR).
The range is calculated by subtracting the minimum value from the maximum value in the dataset.
In this case, the minimum grade is 85 and the maximum grade is 99, so the range is 99 - 85 = 14.
The interquartile range (IQR) measures the spread of the middle 50% of the data, which is the difference between the first quartile (25th percentile) and the third quartile (75th percentile).
To find the IQR, we need to first arrange the data in ascending order:
85, 88, 90, 90, 92, 92, 95, 96, 99.
The first quartile (Q1) represents the 25th percentile, so we need to find the value that is 25% into the dataset. Since we have nine data points, 25% of 9 is 2.25. We can interpolate to find that Q1 is between the second and third values in the dataset: 88 and 90. Therefore, Q1 is 88.
Similarly, the third quartile (Q3) represents the 75th percentile, which is 75% into the dataset. Again, 75% of 9 is 6.75. We can interpolate to find that Q3 is between the sixth and seventh values in the dataset: 92 and 95. Therefore, Q3 is 92.
Now, we can calculate the IQR by subtracting Q1 from Q3: 92 - 88 = 4.
Comparing the range (14) and IQR (4), we can see that the IQR is smaller and measures the spread of the middle 50% of the data, making it a better measure of variability for this dataset.