The mean of 5 observations is 20. If another observation is added, then the mean increases by 2. What is the value of the 6th observation that is added?

Correct option is B

Given:

The mean of 5 observations is 20.
When a 6th observation is added, the mean increases by 2.
Formula Used:

Mean of observations:  Mean  =  $$\frac{\text{Sum of Observations}}{\text{Number of Observations}}$$​​
New Mean after adding 6th observation:  $$\text{New Mean} = \text{Original Mean} + 2$$   

Solution:

Calculate the Sum of the First 5 Observations:

Since the mean of 5 observations is 20, the sum of the first 5 observations is:

Sum of 5 observations = $$5 \times 20 = 100$$​​

Set Up the Equation for the New Mean:

When the 6th observation is added, the new mean becomes 20 + 2 = 22

The mean of 6 observations is given by:

​$$\text{New Mean} = \frac{\text{Sum of 6 observations}}{6}$$​​

Substitute the values:

​$$22 = \frac{100 + x}{6}$$​​
where x is the 6th observation.

Solve for the 6th Observation (x):

Multiply both sides by 6:

 $$22 \times 6 = 100 + x$$​
132 = 100 + x
x = 132 - 100
x = 32