Question

Find the standard deviation for the following data
X 10 15 18 20 25
Y 3 2 5 8 2

Answer 1

Answer:

1.4142

Step-by-step explanation:

First we obtain the covariance between the two variables X and Y as follows

the sample mean of X is

$\bar x=\frac{10+15+18+20+25}{5}=17.6$

the sample mean of Y is

$\bar y=\frac{3+2+5+8+2}{5}=4$

Then, covariance is computed as;

$cov(x,y)=\frac{1}{n-1}*\sum(xi-\bar x)(y_i-\bar y)\\ =\frac{1}{5-1} *[(10-17.6)(3-4)+(15-17.6)(2-4)+(18-17.6)(5-4)+(20-17.6)(8-4)+(25-17.6)(2-4)\\=\frac{1}{4} *8\\=2$

The square root of this gives us the standard deviation of the dataset

$SD=\sqrt{2}\\ =1.4142$