Explanation
Step 1: Convert percentages to decimals
Returns: 0.21, 0.17, 0.11, 0.18, 0.15
Step 2: Calculate sample mean
xΛ=50.21+0.17+0.11+0.18+0.15β=50.82β=0.164
Step 3: Calculate sum of squared deviations
β(xiββxΛ)2=(0.21β0.164)2+(0.17β0.164)2+(0.11β0.164)2+(0.18β0.164)2+(0.15β0.164)2
=(0.046)2+(0.006)2+(β0.054)2+(0.016)2+(β0.014)2
=0.002116+0.000036+0.002916+0.000256+0.000196
=0.00552
Step 4: Calculate unbiased sample variance
s2=nβ1β(xiββxΛ)2β=40.00552β=0.00138
Therefore, the correct unbiased sample variance is 0.00138.