Answer:
a). Arithmetic average return=12.80%
b). The variance of the company's returns=116.2
c). Standard deviation=10.78
Explanation:
a). The arithmetic average return can be expressed as;
Arithmetic average return=Sum of returns/Number of returns
where;
Sum of returns=8%+(-15%)+19%+31%+21%=64
Number of returns=5
replacing;
Arithmetic average return=64/5=12.80%
b). Variance of the company's returns
Step 1: Write down formula for variance
Variance=∑(Xi-X)²/n-1
where;
Xi=term in data set
X=sample mean
∑=sum
n=sample size
Step 2: write down each data set
X1=8%, X2=-15%, X3=19%, X4=31%, X5=21%
Step 3: Subtract the mean from each data set
Take the absolute value of each data
X1-X=8-12.8=-4.8
X2-X=15-12.8=2.2
X3-X=19-12.8=6.2
X4-X=31-12.8=18.2
X5-X=21-12.8=8.2
Step 4: Square each result and sum
∑(Xi-X)²=4.8²+2.2²+6.2²+18.2²+8.2²=464.8
Step 5: Divide by n-1
n=number of data points=5
n-1=5-1=4
∑(Xi-X)²/n-1=464.8/4=116.2
The variance of the company's returns=116.2
c). Standard deviation=√variance=√116.2
Standard deviation=10.78
