During bioconversion of sucrose to citric acid by Aspergillus niger,
final samples of 6 batches of fermentation broth were analyzed for citric acid content.
The results (in g/L) were found to be
47.3, 52.2, 49.2, 52.4, 49.1 and 46.3.
Q.55
The standard deviation for the above results is
Options:
(A) 2.49
(B) 3.0
(C) 1.84
(D) 5.91
Introduction
In industrial biotechnology, statistical tools such as standard deviation are used to evaluate
batch-to-batch variation during fermentation processes. In the bioconversion of sucrose to citric acid
by Aspergillus niger, analyzing variability ensures process consistency and product quality.
Problem Statement
Six batches of fermentation broth were analyzed for citric acid content (g/L):
47.3, 52.2, 49.2, 52.4, 49.1, 46.3
Find the standard deviation of the above results.
Step 1: Calculation of Mean
Mean (x̄) =47.3 + 52.2 + 49.2 + 52.4 + 49.1 + 46.3 /6
Mean (x̄) =296.5 /6
= 49.42 g/L
Step 2: Deviation from Mean
| Observation (x) | x − x̄ | (x − x̄)2 |
|---|---|---|
| 47.3 | -2.12 | 4.49 |
| 52.2 | 2.78 | 7.73 |
| 49.2 | -0.22 | 0.05 |
| 52.4 | 2.98 | 8.88 |
| 49.1 | -0.32 | 0.10 |
| 46.3 | -3.12 | 9.73 |
Sum of (x − x̄)2 = 30.98
Step 3: Standard Deviation Formula
Since the data represents a sample, sample standard deviation is used:
SD = √Σ(x − x̄)2 /n − 1
SD = √30.98 /5
SD = √6.196 ≈ 2.49
Correct Answer
Option (A): 2.49
Conclusion
The standard deviation of citric acid concentration produced by
Aspergillus niger is 2.49 g/L, indicating moderate batch-to-batch variation
in the fermentation process.
