average

Examples of average in the following topics:

• Average and Marginal Cost

  • It is also equal to the sum of average variable costs and average fixed costs.
  • Economists analyze both short run and long run average cost.
  • When the average cost declines, the marginal cost is less than the average cost.
  • When the average cost increases, the marginal cost is greater than the average cost.
  • When the average cost stays the same (is at a minimum or maximum), the marginal cost equals the average cost.

• Average Velocity: A Graphical Interpretation

  • His average velocity would be:
  • To illustrate the difference between average speed and average velocity, consider the following additional example .
  • From this, you would get an average speed of 14/30 = 0.47 m/s.
  • Therefore, your average velocity, or displacement over time, would be 0 m/s.
  • If you started walking from one corner and went all the way around the rectangle in 30 seconds, your average speed would be 0.47 m/s, but your average velocity would be 0 m/s.

• Average Cost Method

  • Under the Average Cost Method, It is assumed that the cost of inventory is based on the average cost of the goods available for sale during the period.
  • Under the average cost method, it is assumed that the cost of inventory is based on the average cost of the goods available for sale during the period.
  • There are two commonly used average cost methods: Simple Weighted Average Cost method and Moving-Average Cost method.
  • The following is an example of the weighted average cost method:
  • The Weighted-Average Method of inventory costing is a means of costing ending inventory using a weighted-average unit cost.

• Calculating and Understanding Average Returns

  • Average returns are commonly found using average ROI, CAGR, or IRR.
  • The average ROI is the arithmetic average: divide the total ROI by the number of periods.
  • This is a simple way to calculate the average return.
  • Average ROI generally does not calculate the actual average rate of return, because it does not incorporate compounding returns.
  • CAGR, unlike average ROI, does consider compounding returns.

• Average Atomic Mass

  • The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance.
  • To calculate the average mass, first convert the percentages into fractions (divide them by 100).
  • Average atomic mass of chlorine = (0.7577 $\cdot$ 35 amu) + (0.2423 $\cdot$ 37 amu) = 35.48 amu
  • Average atomic mass of boron = (0.199 $\cdot$  10 amu) + (0.801 $\cdot$  11 amu) = 10.80 amu
  • Calculate the average atomic mass of an element given its isotopes and their natural abundance

• Average Value of a Function

  • The average of a function $f(x)$ over an interval $[a,b]$ is $\bar f = \frac{1}{b-a} \int_a^b f(x) \ dx$.
  • An average is a measure of the "middle" or "typical" value of a data set.
  • However, the concept of average can be extended to functions as well.
  • Note that the average is equal to the area under the curve, $S$, divided by the range:
  • Evaluate the average value of a function over a closed interval using integration

• Expected Values of Discrete Random Variables

  • The expected value of a random variable is the weighted average of all possible values that this random variable can take on.
  • The weights used in computing this average are probabilities in the case of a discrete random variable.
  • If all outcomes $x_i$ are equally likely (that is, $p_1 = p_2 = \dots = p_i$), then the weighted average turns into the simple average.
  • This is intuitive: the expected value of a random variable is the average of all values it can take; thus the expected value is what one expects to happen on average.
  • If the outcomes $x_i$ are not equally probable, then the simple average must be replaced with the weighted average, which takes into account the fact that some outcomes are more likely than the others.

• Inventory Techniques

  • FIFO, LIFO, and average cost methods are accounting techniques used in managing inventory.
  • Average cost method is quite straightforward.
  • It takes the weighted average of all units available for sale during the accounting period and then uses that average cost to determine the value of COGS and ending inventory.
  • There are two commonly used average cost methods: Simple weighted average cost method and moving average cost method.
  • This gives a Weighted Average Cost per Unit.

• Using the Receivables Turnover Ratio

  • $\dfrac{\text{Trade receivables}}{\text{Credit sales} \cdot 365} = \text{Average collection period in days}$
  • Finally, the average creditor payment period can be calculated as follows:
  • $\dfrac{\text{Trade payables}}{\text{Credit purchases} \cdot 365} = \text{Average payment period in days}$

• Comparing Marginal and Average Tax Rates

  • Taxes can be evaluated based on an average impact or a marginal impact and can be categorized as progressive, regressive, or proportional.
  • An average tax rate is the ratio of the total amount of taxes paid, T, to the total tax base, P, (taxable income or spending), expressed as a percentage.
  • If a company pays different rates on the first $100,000 in earning than the next $100,000, it will sum up the total tax paid and divide it by $200,000 to calculate the average tax rate.
  • A regressive tax is a tax imposed in such a manner that the average tax rate decreases as the amount subject to taxation increases .
  • "Regressive" describes a distribution effect on income or expenditure, referring to the way the rate progresses from high to low, where the average tax rate exceeds the marginal tax rate.