Mrs. Rodriguez randomly surveyed 15 of her ninth grade students on how many hours they spent completing assignments and preparing for assessments last week:
0.5 0.5 1.0 1.5 1.5 1.5 2 2 2.5 3 3 3.5 5 8 10
Which measure of variability—range or IQR—best describes the spread of the dataset? Enter 1 for range or 2 for IQR.
2 for IQR
To determine which measure of variability best describes the spread of the dataset, we need to compare the range and the interquartile range (IQR).
1. Range: The range is the difference between the maximum and minimum values in the dataset. To calculate the range, we find the maximum value and subtract the minimum value.
2. IQR: The interquartile range (IQR) is a measure of statistical dispersion. It is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3).
Let's calculate both measures and compare them:
1. Range: The maximum value is 10 and the minimum value is 0.5. So, the range is 10 - 0.5 = 9.5.
2. IQR: To calculate the IQR, we first need to find the values of Q1 and Q3.
- Q1: The median of the lower half of the dataset. Since there are 15 data points, the median is the 8th value when arranged in ascending order. In this case, the 8th value is 2.
- Q3: The median of the upper half of the dataset. In this case, the 8th value is also 2.5.
Now, we can calculate the IQR by subtracting Q1 from Q3: 2.5 - 2 = 0.5.
Comparing the range (9.5) and IQR (0.5), we can conclude that the IQR best describes the spread of the dataset. Therefore, the answer is 2 for IQR.