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 3 8 13 18 23
f 7 10 15 10 8

x 3

8

13 18 23 f 7 10 15 10

8