Question

The arithmetic mean of the 6 observations was found to be 36. If one more observation 22 is to be added to the data, then what would be a new mean of the data?

• A. 216
• B. 34
• C. 240
• D. 36

Answer 1

The correct option is B 34

Mean of the 6 observations $\left(\overline{x}\right)$ = 36

Number of observations (N) = 6

We know that,

Mean $\left(\overline{x}\right)$ = $\frac{\sum x_i}{N}$

36 = $\frac{\sum x_i}{6}$

$\sum x_i$ = $36\times 6$ = 216

New observation 22 is added.
Sum of 7 observations $\sum x_i$ = 216 +22 = 238
Mean of 7 observations $\overline{x}$ = $\frac{238}{7}$ = 34