Which describes how to calculate the range of this data set?
4, 5, 6, 8, 11, 12
The Correct Answer and Explanation is:
To calculate the range of a data set, you subtract the smallest value from the largest value. The range gives you an idea of how spread out the data is.
Here are the steps to calculate the range of the data set: 4, 5, 6, 8, 11, 12.
Steps:
- Identify the largest and smallest values in the data set.
- The smallest value is 4.
- The largest value is 12.
- Subtract the smallest value from the largest value.
[
\text{Range} = \text{Largest Value} – \text{Smallest Value}
]
[
\text{Range} = 12 – 4 = 8
] - Interpret the result.
- The range of this data set is 8. This means that the spread between the smallest and largest values is 8 units.
Why is the range useful?
- The range is a simple and quick way to understand the variability of the data set.
- It gives an idea of how far apart the extreme values are from each other.
- However, the range has limitations. It is sensitive to outliers, or extreme values. If there is an extremely high or low value in the data set, it could drastically increase the range and make it less representative of the overall spread of the data.
Example:
If the data set were 4, 5, 6, 8, 11, 100, the range would be:
[
\text{Range} = 100 – 4 = 96
]
This larger range would suggest that the presence of 100 is creating a much wider spread than most of the other values, which could distort the true distribution of the data. Therefore, while the range provides valuable information about the overall spread, other measures like the interquartile range (IQR) might be used for a more detailed understanding of variability, especially when outliers are present.
In conclusion, for the given data set, the range is 8, which is the difference between the largest (12) and the smallest (4) values.