Activity- statistics problems

=Problem 1= If n =10, $$\bar x $$  =  12 and $$\sum{x^2}= 1530 find the standard deviation $$

=INTERPRETATION OF PROBLEM=

=Previous knowledge=

=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= Problem No.1 of excercise No.6.1 Find the Standard deviation for the following data.

=INTERPRETATION OF PROBLEM=

=Previous knowledge=

=Solution:=

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

=Problem 3= Problem No.5 of excercise No.6.3 Find the varience and Standard deviation for the following data.

=INTERPRETATION OF PROBLEM=

=Previous knowledge=

=Solution:= A=assumed average. c=4 d=$$\frac{x-A}{c}$$=$$\frac{32-40}{4}$$=$$\frac{-8}{4}=-2$$

assumed mean A=$$\frac{\sum fx}{n}$$=$$\frac{1668}{40}=41.7$$

Varience σ²=[$$\frac{\sum {fd^2}}{n}-({\frac{\sum fx}{n})^2}]c^2$$

σ²=[$$\frac{85}{40}-({\frac{17}{40})^2}]4^2$$

σ²=[2.125-0.180]16

σ²=[1.945]16

σ²=31.12 standard deviation, σ=$$\sqrt{varience}$$ σ=$$\sqrt{31.12}$$ σ=5.58