Final Answer:
The average, range, and deviation provide essential insights into the dataset's central tendency, spread, and variability. The average represents the typical value, the range showcases the spread between the maximum and minimum values, while the deviation measures how data points vary from the mean.
Step-by-step explanation:
The average, also known as the mean, is the sum of all values in a dataset divided by the number of data points. It serves as a measure of central tendency, indicating the typical or central value within the dataset. For instance, in a set of test scores, the average score provides an idea of the typical performance of the students.
On the other hand, the range represents the difference between the highest and lowest values in the dataset. It measures the dispersion or spread of data points. For example, in a sales report, the range highlights the extent between the lowest and highest sales figures, indicating the variability in performance or revenue.
Deviation, specifically standard deviation or variance, illustrates how much individual data points deviate from the average. It quantifies the dispersion or variability of the dataset. A higher deviation implies more significant variability among the data points, while a lower deviation indicates data points are closer to the mean. In finance, standard deviation helps assess the volatility of stock prices, where higher standard deviation signifies riskier investments due to price fluctuations.
In summary, the average provides a central value, the range shows the spread of values, and the deviation measures the variability from the mean, all contributing crucial information to understand the characteristics and distribution of a dataset in various contexts.