Question

Refer to Q9 and calculate the variance of each data set?

(a) (1239,8.0)

(b) (1823,8.9)

(c) (8.9,1823)

(d) (8.0,1239)

I have been asked this question by my college director while I was bunking the class.

My doubt is from Graph Paper with Logarithmic Coordinates topic in portion Presentation and Analysis of Data of Bioprocess Engineering

Answer 1

The correct answer is (b) (1823,8.9)

The explanation: In variance there is small culture and bulk culture.

Small culture-

The sum of values in the (X-x̅)^2 column = Ƹ(X-x̅)^2 = 16,403

Since there are 10 samples in this data set, n=10. Placing these values into the formula for calculating the variance yields,

Variance = \(\frac{Ƹ(X-x̅)^2}{n-1} = \frac{16.403}{10-1}\)

=  \(\frac{16.403}{9}\)

=  1823

Bulk culture-

The sum of values in the (X-x̅)^2 column = Ƹ(X-x̅)^2 = 80

Since there are 10 samples in this data set, n=10. Placing these values into the formula for calculating the variance yields,

Variance = \(\frac{Ƹ(X-x̅)^2}{n-1} = \frac{80}{10-1}\)

= \(\frac{80}{9}\)

= 8.9