Understanding the Coefficient of Range in Statistical Analysis

The question asks for the "coefficient of expansion" given the highest and lowest values of a data series. In the context of statistics, this is commonly referred to as the Coefficient of Range. The Coefficient of Range is a measure of dispersion, indicating the relative difference between the extreme values of a data set.

To calculate the Coefficient of Range, we use the formula:

\(\text{Coefficient of Range} = \frac{\text{Highest Value} - \text{Lowest Value}}{\text{Highest Value} + \text{Lowest Value}}\)

In this specific data series, we are given:

• Highest Value = 40
• Lowest Value = 20

Now, let's perform the statistics calculation using these values to find the Coefficient of Range.

Calculating the Coefficient of Range

Using the range formula:

\(\text{Coefficient of Range} = \frac{40 - 20}{40 + 20}\)

First, calculate the numerator (the Range):

\(\text{Range} = 40 - 20 = 20\)

Next, calculate the sum of the highest and lowest values:

\(\text{Sum of Extremes} = 40 + 20 = 60\)

Now, divide the Range by the sum of the extreme values:

\(\text{Coefficient of Range} = \frac{20}{60}\)

Simplify the fraction:

\(\text{Coefficient of Range} = \frac{1}{3}\)

Thus, the Coefficient of Range for this data series is \(\frac{1}{3}\). This statistical coefficient helps understand the variability relative to the total spread of the data.

Result of the Statistical Calculation

Based on the calculation, the coefficient is \(\frac{1}{3}\).

This result corresponds to one of the provided options.