What Is a Mean?

A mean is the mathematical average of two or more numbers. It can be computed using the 澳洲幸运5开奖号码历史查询:arithmetic mean method, which uses the sum of the numbers in the series, and the 澳洲幸运5开奖号码历史查询:geometric mean method, which is the aꦇverage of a set 💮of products.

Arithmetic Mean

The arithmetic mean is the simple average or sum of a series of numbers di🍒vided by the count of that series of numbers. For example, the arithmetic mean of the numbers 4 and 9 is found by adding 4 and 9 and then dividing by 2 (the qﷺuantity of numbers). The arithmetic mean in this example is 6.5.

A = 4+9/2

Arithmetric Mean = 6.5

Geometric Mean

T𝕴he geometric mean uses a more complex formula. To calculate the geometric mean, multiply all values within a dataset. Then, take the root of the sum equal to the number of values within that dataset.

To calculate the geometric mean of the values 4 and 9:

• Multiply 4x9 = 36
• Take the square root of 36
• Geometric Mean = 6

Calculating Returns

Examine the price of a stock over a 10-day period. Imagine an investor purchased one share of stock for👍 $148.01.

$\begin{aligned}\text{Arithmetic Mean} &= \tiny{\frac{ (0.0045) + 0.0121 + 0.0726 + ... + 0.0043 + (0.0049) + 0.0376 }{ 10 } } \\&= 0.0067 \\&= 0.67\% \\\end{aligned}$Arithmetic Mean​=10(0.0045)+0.0121+0.0726+...+0.0043+(0.0049)+0.0376​=0.0067=0.67%​

$\begin{aligned}\text{Geometric Mean} &= \tiny{\sqrt[10]{ 0.9955 \times 1.0121 \times 1.0726 \times ... \times 1.0043 \times 0.9951 \times 1.0376 } - 1} \\&= 0.0061 \\&= 0.61\% \\\end{aligned}$Geometric Mean​=100.9955×1.0121×1.0726×...×1.0043×0.9951×1.0376​−1=0.0061=0.61%​

The arithmetic mean is 0.67%: th🌼e total of the returns divided bꩵy 10. However, the arithmetic mean of returns is only accurate when there is no volatility in the market.

When the arithmetic mean of 0.67% is applied to each sto𒉰ck price, the end value is $152.63. However, the stock traded for $157.32 on the last♒ day. This means that the arithmetic mean of returns is understated.

The geometric mean factors in 澳洲幸运5开奖号码历史查询:compounding and volatility. Because it is impossible to take the root of a negative value, add one to all the percentage returns so that the product total yields a positive number. Take the 10th root of this number and subtract from one to get the ꧟percenta🍒ge figure. The geometric mean of returns for the investor in the final five days is 0.61%.

When each closing price is raised by the geometric average return of 0.61%, the answer is $157.32. The geometric mean is a more accurate reflection of the true return of a 澳洲幸运5开奖号码历史查询:portfolio.

Why Means Matter to Investors

The mean is a statistical indicator used to gauge performance over time. Specific to investing, the mean is used to understand the performance of a company’s stock price over daysඣ, months, or years. Within business and investing, the mean is used extensively to:

• Determine whether an equity trades above or below its average over a specified period.
• Compare the average 澳洲幸运5开奖号码历史查询:rate of return for broad markets during prior 澳洲幸运5开奖号码历史查询:recessions or inflationary periods to guide decision-making.
• See whether trading volume or the quantity of market orders aligns with market activity.
• Analyze the operational performance of a company. Some financial ratios like 澳洲幸运5开奖号码历史查询:days sales outstanding require determining the average 澳洲幸运5开奖号码历史查询:accounts receivable balance for the numerator.
• Quantify 澳洲幸运5开奖号码历史查询:macroeconomic data like average unemployment over time to determine the general health of an economy.

The Bottom Line

The mean is another word for a mathematical average. The simple or arithmetic mean is the average calculated by summing up the values of some observations and dividing by the number of observations. The geometric mean is calculated by multiplying all the numbers in a dataset and then taking the nth root oꦇf the product, where n is the total number of values in the dataset.