Question

The arithmetic mean of 10 numbers is 4, when an eleventh number, x is added so that the overall mean is changed to 5. When a twelfth number, y is added the mean changes to 4. Determine the values of x and y

Answer 1

Answer on Question #85572 – Math – Statistics and Probability

Question

The arithmetic mean of 10 numbers is 4, when an eleventh number, $x$ is added so that the overall mean is changed to 5. When a twelfth number, $y$ is added the mean changes to 4. Determine the values of $x$ and $y$

Solution

Since the arithmetic mean of $N$ numbers is $m = \frac{\sum_{i=1}^{N} x_i}{N}$, then $\sum_{i=1}^{N} x_i = mN$.

Therefore, the sum of 10 numbers is $4 * 10 = 40$.

Then the sum of 11 numbers is equal to $5 * 11 = 55$.

It follows that $x = 55 - 40 = 15$.

The sum of 12 numbers is equal to $4 * 12 = 48$.

Then $y = 48 - 55 = -7$.

Answer:

$$x = 15, y = -7$$

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