Question

Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been made by counting the bacteria in each of 6randomly chosen specimens of ocean water (of a fixed size). The 6 counts obtained were as follows.48, 67, 64, 61, 63, 69Send data to calculatorFind the standard deviation of this sample of numbers. Round your answer to two decimal places.

Answer 1

σ =6.78

Count, N:6

Sum, Σx:372

Mean, μ:62

The standard deviation(σ) can be calculated using the formula below:

$\sigma=\sqrt[]{\frac{1}{N}\sum ^n_{i=1}(x_i-\mu)^2}$

To calculate Mean( μ);

$\text{Mean}=\frac{48+67+64+61+63+69}{6}$

Mean( μ) = 62

$\sigma=\sqrt[]{\frac{(48-62)^2+(67-62)^2+(64-62)^2+(61-62)^2+(63-62)^2+(69-62)^2}{6}}$

$=\sqrt[]{\frac{276}{6}}$

$=\sqrt[]{46}$

$=6.78$

Therefore, the standard deviation(σ) = 6.78