Variance Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
Two investments have the same mean return of 8%. Investment A returns: {6,7,8,9,10}%\{6, 7, 8, 9, 10\}\%. Investment B returns: {2,5,8,11,14}%\{2, 5, 8, 11, 14\}\%. Calculate the variance of each and interpret.

Solution

  1. 1
    Both have ฮผ=8%\mu = 8\%. Calculate variance for A: deviations are โˆ’2,โˆ’1,0,1,2-2,-1,0,1,2; squared: 4,1,0,1,44,1,0,1,4; sum =10= 10; ฯƒA2=10/5=2\sigma_A^2 = 10/5 = 2
  2. 2
    Calculate variance for B: deviations are โˆ’6,โˆ’3,0,3,6-6,-3,0,3,6; squared: 36,9,0,9,3636,9,0,9,36; sum =90= 90; ฯƒB2=90/5=18\sigma_B^2 = 90/5 = 18
  3. 3
    Compare: ฯƒB2=18>ฯƒA2=2\sigma_B^2 = 18 > \sigma_A^2 = 2, so Investment B is 9 times more variable
  4. 4
    Interpret: Both earn 8% on average, but B is far riskier โ€” returns fluctuate much more widely

Answer

ฯƒA2=2\sigma_A^2 = 2, ฯƒB2=18\sigma_B^2 = 18; Investment B carries substantially more risk.
Variance is a key measure of financial risk. Same average return does not mean same risk. Higher variance means returns are less predictable, which matters for risk-averse investors.

About Variance

The variance is the average of the squared deviations from the mean: ฯƒ2=1nโˆ‘(xiโˆ’xห‰)2\sigma^2 = \frac{1}{n}\sum (x_i - \bar{x})^2. It is the square of the standard deviation.

Learn more about Variance โ†’

More Variance Examples

Example 1 medium

Calculate the population variance for the data set: [formula].

Example 3 easy

Calculate the population variance for: [formula].

Example 4 medium

A data set has [formula] values with mean [formula] and [formula]. Find the variance using the compu

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