To determine which measure of variability, IQR (Interquartile Range) or MAD (Mean Absolute Deviation), best describes the spread of the dataset, we should consider the characteristics of the data.
First, let's evaluate the dataset:
Data: 7.75, 8.00, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00, 10.00, 10.00, 10.25, 10.50, 10.75
To compute IQR:
- Arrange the data in ascending order (already done).
- Find the first (Q1) and third (Q3) quartiles:
- Q1 is the median of the first half of the data.
- Q3 is the median of the second half of the data.
- IQR = Q3 - Q1.
To compute MAD:
- Find the mean of the data.
- Calculate the absolute deviations from the mean.
- Find the average of those absolute deviations.
However, without the need to calculate explicitly, for datasets with outliers or skewed distributions, IQR is generally a more robust measure of spread since it is not affected by extreme values. In this dataset, 7.75 is much lower than the other values, which could skew the mean and MAD somewhat.
Since the dataset appears to have a low degree of skewness and is relatively tight with most values clustered together, IQR would be the most appropriate measure of variability to describe the spread.
Therefore, the answer is:
1 for IQR.