Respuesta :
Answer:
option (c) The mean age will stay the same but the variance will decrease
Step-by-step explanation:
Case I: For 3 executives of ages 56, 57 and 58
Number of executives, n = 3
Mean = [tex]\frac{\textup{56 + 57 + 58 }}{\textup{3}}[/tex]
or
Mean = 57
Variance = [tex]\frac{\sum{(Data - Mean)^2}}{\textup{n-1}}[/tex]
or
Variance = [tex]\frac{(56 - 57)^2+(57-57)^2+(58-57)^2}{\textup{3-1}}[/tex]
or
Variance = [tex]\frac{1+0+1}{\textup{2}}[/tex]
or
Variance = 1
For Case II: For 4 executives of ages 56, 57, 58 and 57
Number of executives, n = 4
Mean = [tex]\frac{\textup{56 + 57 + 58 + 57 }}{\textup{4}}[/tex]
or
Mean = 57
Variance = [tex]\frac{\sum{(Data - Mean)^2}}{\textup{n-1}}[/tex]
or
Variance = [tex]\frac{(56 - 57)^2+(57-57)^2+(58-57)^2+(57-57)^2}{\textup{4-1}}[/tex]
or
Variance = [tex]\frac{1+0+1+0}{\textup{3}}[/tex]
or
Variance = 0.67
Hence,
Mean will remain the same and the variance will decrease
Hence,
The correct answer is option (c) The mean age will stay the same but the variance will decrease
