# Find the covariance s_(xy) using bivariate data.

lwfrgin 2021-01-04 Answered
Find the covariance ${s}_{xy}$ using bivariate data.
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## Expert Answer

Macsen Nixon
Answered 2021-01-05 Author has 117 answers

The given bivariate data is(1,6),(3,2),and(2,4).
Calculation:
First determine $\sum {x}_{i}{y}_{i},\sum {x}_{i}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\sum {y}_{i}$.
${x}_{i}\to$ first coordinates of the ordered pairs.
${y}_{i}\to$ second coordinates of the ordered pairs.
$\sum {x}_{i}{y}_{i}=1\cdot 6+3\cdot 2+2\cdot 4=20$
$\sum {x}_{i}=1+3+2=6$
$\sum {y}_{i}=6+2+4=12$
For covariance .
Where n = number of ordered pairs.
n=3
${s}_{xy}=\frac{20-\frac{6\cdot 12}{3}}{3-1}$
$=\frac{20-\frac{72}{3}}{3-1}$
$=\frac{2-24}{2}$
$=-\frac{4}{2}=-2$
Hence ${s}_{xy}=-2$.

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