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 5 randomly chosen specimens of ocean water (of a fixed size). the 5 counts obtained were as follows. 49, 53, 64, 61, 53. send data to calculator. find the standard deviation of this sample of numbers. round your answer to two decimal places. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{49 + 53+64+61+53}{5}=\frac{280}{5}=56$

Step2: Calculate the squared - differences

$(49 - 56)^2=(-7)^2 = 49$
$(53 - 56)^2=(-3)^2 = 9$
$(64 - 56)^2=8^2 = 64$
$(61 - 56)^2=5^2 = 25$
$(53 - 56)^2=(-3)^2 = 9$

Step3: Calculate the sum of squared - differences

$S=\sum_{i = 1}^{n}(x_i-\bar{x})^2=49 + 9+64+25+9=156$

Step4: Calculate the sample variance

$s^2=\frac{S}{n - 1}=\frac{156}{5 - 1}=\frac{156}{4}=39$

Step5: Calculate the sample standard deviation

$s=\sqrt{s^2}=\sqrt{39}\approx6.24$

Answer:

$6.24$