The mean of 10 observations is 5. If 2 is added to each observation and then multiplied by 3, then what will be the new mean?
(a)5
(b)7
(c)15
(d)21

Options

A. 5
B. 7
C. 15
D. 21

Answer

To solve the problem step by step, we will follow the operations described in the question and apply them to the mean.

### Step 1: Identify the initial mean
The mean of the 10 observations is given as 5.

### Step 2: Add 2 to each observation
According to the problem, we need to add 2 to each observation. Since the mean is a measure that represents the average of all observations, we can also add 2 to the mean:
- New mean after addition = Initial mean + 2
- New mean after addition = 5 + 2 = 7

### Step 3: Multiply the new mean by 3
Next, we need to multiply the new mean by 3:
- New mean after multiplication = New mean after addition × 3
- New mean after multiplication = 7 × 3 = 21

### Final Answer
Thus, the new mean after performing the operations is **21**.