The difference between the largest and the smallest data values is the
a. variance
b. interquartile range
c. range
d. coefficient of variation
The correct answer and explanation is :
The correct answer is c. range.
Explanation:
In statistics, the range is a measure of how spread out the values in a data set are. It is calculated by finding the difference between the largest and smallest values in the data set.
Formula for Range:
$$
\text{Range} = \text{Largest value} – \text{Smallest value}
$$
The range provides a simple and quick way to understand the extent of variation in a data set. However, it does not give information about how the data points are distributed between the largest and smallest values. For example, if a dataset has an outlier or extreme values, the range will be heavily influenced by those values, which may not reflect the overall distribution of the data.
Comparison with Other Terms:
- Variance (Option a): Variance is a measure of how much individual data points differ from the mean of the data set. It is calculated as the average of the squared differences between each data point and the mean. Variance provides insight into the spread of the data around the mean but is not directly related to the difference between the maximum and minimum values.
- Interquartile Range (Option b): The interquartile range (IQR) is a measure of statistical dispersion, defined as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data. The IQR describes the range within which the middle 50% of data points fall, offering a more robust measure of spread that is less sensitive to outliers than the range.
- Coefficient of Variation (Option d): The coefficient of variation is a measure of the relative variability of a data set. It is calculated by dividing the standard deviation by the mean and is often expressed as a percentage. The coefficient of variation is particularly useful when comparing the variability of data sets with different units or means, but it does not directly relate to the difference between the largest and smallest data points.
In summary, the range is the most straightforward measure of the spread of data based on the largest and smallest values, making option c the correct choice.