Question

There are three executives in an office, ages 56, 57, and 58. If a 57-year-old executive enters the room, the

Answer 1

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 = $\frac{\textup{56 + 57 + 58 }}{\textup{3}}$

or

Mean = 57

Variance = $\frac{\sum{(Data - Mean)^2}}{\textup{n-1}}$

or

Variance = $\frac{(56 - 57)^2+(57-57)^2+(58-57)^2}{\textup{3-1}}$

or

Variance = $\frac{1+0+1}{\textup{2}}$

or

Variance = 1

For Case II: For 4 executives of ages 56, 57, 58 and 57

Number of executives, n = 4

Mean = $\frac{\textup{56 + 57 + 58 + 57 }}{\textup{4}}$

or

Mean = 57

Variance = $\frac{\sum{(Data - Mean)^2}}{\textup{n-1}}$

or

Variance = $\frac{(56 - 57)^2+(57-57)^2+(58-57)^2+(57-57)^2}{\textup{4-1}}$

or

Variance = $\frac{1+0+1+0}{\textup{3}}$

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