Question

A stamp collecting club calculated that the average (arithmetic mean) number of stamps in its members $10$ collections was $88$. However, it was discovered that $2$ numbers in the calculations were entered incorrectly. The number $55$ was entered as $75$ and the number $78$ as $88$. What is the correct average number of stamps in the $10$ collections?

• A. $91$
• B. $89$
• C. $87$
• D. $86$
• E. $85$

Answer 1

Answer: (E)

$85$

Given, number of collections $=$ $10$

Average number of stamps in the $10$ collections $=$ $88$

However, $2$ numbers are entered incorrectly.

$55$ is entered as $75$

$78$ is entered as $88$

Now, let us assume the total number of stamps in the remaining $8$ collections other than the above $2$ collections be ${}^{\prime }{x}^{\prime }$.

As Initial average number of stamps in the $10$ collections $=$ $88$

$\frac{\text{Total number of stamps in 10 collections}}{\text{Number of collections}}$ $=$ $88$

$\Rightarrow \frac{x+75+88}{10}$ $=$ $88$

$\Rightarrow x$ $+$ $75$ $+$ $88$ $=$ $88$ $\times$ $10$

$\Rightarrow x$ $+$ $75$ $+$ $88$ $=$ $880$

$\Rightarrow x$ $=$ $880$ $-$ $163$

$\Rightarrow x$ $=$ $717$

Now, to find ${}^{\prime }correc{t}^{\prime }$ average number of stamps in the $10$ collections,

Correct average number of stamps in $10$ collections $=$ $\frac{\text{Total number of stamps in 10 collections}}{\text{Number of collections}}$

$=$ $\frac{x+55+78}{10}$

$=$ $\frac{717+55+78}{10}$

$=$ $\frac{850}{10}$

$=$ $85$

Therefore, corrected average number of stamps in $10$ collections is ${}^{\prime }{85}^{\prime }$.