lab 6

problem number 1

x=c(23,9,12,21,24,6,33,34,17,3,12,31,5,10,27,9,15,16,30,38)
N=length(x)
N

## [1] 20

mean_employment=mean(x)
mean_employment ## mean

## [1] 18.75

mean_range=range(x)
mean_range ## range

## [1]  3 38

sigma_2=(sum(x^2)-(sum(x))^2/N)/N
sigma_2 ##variance

## [1] 109.1875

sigma_1=sqrt(sigma_2)
sigma_1 ##standard deviation

## [1] 10.44928

problem number 2

w=c(50,71,57,39,45,64,38,53,35,62,74,40,67,44,77,61,58,55,64,59)
N=length(w)
N

## [1] 20

mean_salary=mean(w)
mean_salary ## mean

## [1] 55.65

mean_range=range(w)
mean_range ## range

## [1] 35 77

sigma_3=(sum(w^2)-(sum(w))^2/N)/N
sigma_3 ##variance

## [1] 146.6275

sigma_4=sqrt(sigma_3)
sigma_4 ##standard deviation

## [1] 12.10898

problem number 3

##calculating mean from a frequecy distibution 
m=c(350,650,950,1250,1550,1850,2150)
f=c(38,105,130,60,42,18,7)
mean_expenditure=sum(m*f)/sum(f)
mean_expenditure

## [1] 983.75

P=sum(f)
P

## [1] 400

sigma_5=(sum(m^2*f)-sum(m*f)^2/P)/P
sigma_5 ##variance

## [1] 169635.9

sigma_6=sqrt(sigma_5) ##standard deviation
sigma_6

## [1] 411.8688