The mean of the numbers 3, 6, 4, x, and 7 is 5. Find the standard deviation.
A
\(\sqrt{2}\)
B
\(\sqrt{3}\)
C
2
D
3
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Standard deviation = \(\frac{\sum(x - \overline{x})^2}{\text{n}}\)
\(\overline{x}\) = \(\frac{ 3 + 6 + 4 + x + 7}{5}\) = 5
= 20 + x = 25
x = 25 - 20 = 5.
x
x - \(\overline{x}\)
(x - \(\overline{x}\))\(^2\)
3
3 - 5
-2 = 4
4
4 - 5
-1 = 1
5
5 - 5
0 = 0
6
6 - 5
1 = 1
7
7 - 5
2 = 4
\(\sum\) (x - \(\overline{x}\))\(^2\) = 10
Standard deviation = \(\frac{\sum(x - \overline{x})^2}{\text{n}}\) = \(\frac{\sqrt{10}}{5}\) = \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #11110)