Question

If the five numbers {3, 4, 7, x, y} have a mean of 5 and a standard deviation of the square root of 2, find x and y given that y > x

Answer 1

Answer on Question #40596, Math, Statistics and Probability

Question:

If the five numbers $\{3, 4, 7, x, y\}$ have a mean of 5 and a standard deviation of the square root of 2, find $x$ and $y$ given that $y \& gt; x$

Solution:

Average value (mean) equals:

$$\frac{3 + 4 + 7 + x + y}{5} = 5$$ $$y + x = 25 - 3 - 4 - 7 = 11$$

For a finite set of numbers, the standard deviation is found by taking the square root of the average of the squared differences of the values from their average value.

$$\sqrt{\frac{(5 - 3)^2 + (5 - 4)^2 + (5 - 7)^2 + (5 - x)^2 + (5 - y)^2}{5}} = \sqrt{2}$$ $$4 + 1 + 4 + (5 - x)^2 + (5 - y)^2 = 10$$ $$(5 - x)^2 + (5 - y)^2 = 1$$

Assuming $y > x$: $x = 5, y = 6$

Answer: $x = 5, y = 6$