Question

The average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34.
The mean value of these temperatures is 4.312.
What is the variance of this data set?

Answer 1

Answer:

0.5192 is the answer

Answer 2

From the mean of the data set and the values given, the variance of the data set is 0.518.

What is variance of a data set?

The variance of a data set is the average of the squared deviations from the mean

The mean of the data = 4.312

Square of deviations:

$(5.0 - 4.312)^{2} = 0.574$

$(3.57 - 4.312)^{2} = 0.550$

$(5.32 - 4.312)^{2} = 1.016$

$(3.19 - 4.312)^{2} = 1.259$

$(3.49 - 4.312)^{2} = 0.675$

$(4.25 - 4.312)^{2} = 0.00384$

$(4.76 - 4.312)^{2} = 0.200$

$(5.19 - 4.312)^{2} = 0.771$

$(3.94 - 4.312)^{2} = 0.138$

$(4.34 - 4.312)^{2} = 0.000784$

Variance = (0.574 + 0.550 + 1.016 + 1.259 + 0.675 + 0.00384 + 0.200 + 0.771 + 0.138 + 0.000784)/ 10

Variance = 0.518

Therefore, the variance of the data set is 0.518

Learn more about variance at: https://brainly.com/question/15858152