Question

do bonds reduce the overall risk of an investment portfolio? let x be a random variable representing annual percent return for the vanguard total stock index (all stocks). let y be a random variable representing annual return for the vanguard balanced index (60% stock and 40% bond). for the past several years, assume the following data. compute the sample mean for x and for y. round your answer to the nearest tenth.

x: 14 0 38 21 32 23 24 -14 -14 -21

y: 10 -2 26 17 22 16 17 -2 -3 -10

\\(\overline{x}=35.5\\) and \\(\overline{y}=12.2\\)

\\(\overline{x}=9.1\\) and \\(\overline{y}=10.3\\)

\\(\overline{x}=10.3\\) and \\(\overline{y}=9.1\\)

\\(\overline{x}=145.0\\) and \\(\overline{y}=10.4\\)

\\(\overline{x}=65.5\\) and \\(\overline{y}=9.5\\)

Explanation:

Step1: Recall sample - mean formula

The sample - mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data points and $n$ is the number of data points. Here $n = 10$ for both $x$ and $y$ data - sets.

Step2: Calculate sum of $x$ values

$\sum_{i=1}^{10}x_{i}=14 + 0+38 + 21+32+23+24+( - 14)+( - 14)+( - 21)=91$

Step3: Calculate sample - mean of $x$

$\bar{x}=\frac{\sum_{i = 1}^{10}x_{i}}{10}=\frac{91}{10}=9.1$

Step4: Calculate sum of $y$ values

$\sum_{i=1}^{10}y_{i}=10+( - 2)+26 + 17+22+16+17+( - 2)+( - 3)+( - 10)=103$

Step5: Calculate sample - mean of $y$

$\bar{y}=\frac{\sum_{i = 1}^{10}y_{i}}{10}=\frac{103}{10}=10.3$

Answer:

$\bar{x}=9.1$ and $\bar{y}=10.3$, so the answer is $\bar{x}=9.1$ and $\bar{y}=10.3$ (the second option).