Activity- statistics problems

Problem 1

If n =10, = 12 and $\sum {x^{2}}=1530findthestandarddeviation$

Solution:

${\frac {\sum x}{n}}={\bar {x}}$

$\sum {x}={{\bar {x}}\times {n}}$

$\sum {x}={12\times {10}}$

$\sum {x}=120$
σ=${\sqrt {{\frac {\sum {x^{2}}}{n}}-({{\frac {\sum x}{n}})^{2}}}}$
σ=${\sqrt {{\frac {1530}{10}}-{144}}}$
σ=${\sqrt {{\frac {1530}{10}}-{144}}}$
σ=${\sqrt {153-144}}$
σ=${\sqrt {9}}$
σ=3

Problem 2

Find the Standard deviation for the following data.

x	03	08	13	18	23
f	07	10	15	10	08

Solution:

x	f	fx	x²	fx²
03	07	021	009	0063
08	10	080	064	0640
13	15	195	169	2535
18	10	180	324	3240
23	08	184	529	4232
	n=50	Σfx=660		Σfx²=10710

Standard deviation σ=${\sqrt {{\frac {\sum {fx^{2}}}{n}}-({{\frac {\sum fx}{n}})^{2}}}}$
σ=${\sqrt {{\frac {10700}{50}}-({{\frac {660}{50}})^{2}}}}$
σ=${\sqrt {214-174.24}}$
σ=${\sqrt {39.96}}$
σ=6.3