Q1ITD - Campbell Biology

Question

The mean (\(\overline x \,\)) of a variable is the sum of the data values divided by the number of observations (n):

                                                     \(\overline x \, = \,\frac{{\sum {{x_i}} }}{n}\)

In this formula, \({x_i}\) is the value of the i th observation of the variable; the \(\sum {} \) symbol indicates that the n values of x are to be added together. Calculate the mean for each treatment.

Step-by-Step Solution

Answer

Treatment	Dose (mg/kg)	Log of number of colonies	Mean (\(\overline x \,\))
Control	-	9.0,9.5,9.0,8.9	9.1
Vancomycin	1.0	8.5,8.4,8.2	8.36
	5.0	5.3,5.9,4.7	5.3
Teixobactin	1.0	8.5,6.0,8.4,6.0	7.22
	5.0	3.8,4.9,5.2,4.9	4.7

Step 1: MRSA (methicillin-resistant Staphylococcus aureus)

MRSA is a type of bacterial infection that occurs by the bacteria Staphylococcus aureus. It spreads by direct contact with the infected people that carry the bacteria.

 

It becomes difficult to treat because of the body’s antibiotic resistance against specific drugs.

Step 2: Treatment by Vancomycin and teixobactin

Vancomycin and teixobactin are the drugs used for the treatment of MRSA (methicillin-resistant staphylococcus aureus). Vancomycin is an antibiotic that reacts with gram-positive bacteria like S. aureus and S. epidermidus.

 

Teixobactin outperforms vancomycin when it comes to killing bacteria like S. aureus and has strong bactericidal action. It also has bactericidal efficacy against S. aureus with intermediate resistance.

Step 3: Calculating the mean value from the given data.

To calculate the mean value, the sum of all colonies obtained is divided by the number of colonies.

 

For the first control treatment, the number of colonies observed was 4 with the values 9.0, 9.5, 9.0, 8.9. Thus,

\(\begin{aligned}{l}{\overline x _{control\,\,}} = \frac{{\sum {9.0 + 9.5 + 9.0 + 8.9} }}{4}\\{\overline x _{control\,\,}} = \frac{{36.4}}{4}\, = \,9.1\end{aligned}\)

 

For the second treatment by vancomycin with 1.0 mg/kg as the dose, the colonies observed were 3 with the values 8.5, 8.4, 8.2. Thus,  

 

\(\begin{aligned}{l}{\overline x _{vancomaycin\,1.0\,\,}} = \frac{{\sum {8.5 + 8.4 + 8.2} }}{3}\\{\overline x _{vancomaycin\,1.0\,\,}} = \frac{{25.1}}{3}\, = \,8.36\end{aligned}\)

 

For the second treatment by vancomycin with 5.0 mg/kg as the dose, the colonies observed were 3 with the values 5.3, 5.9, 4.7. Thus, 

 

\(\begin{aligned}{l}{\overline x _{vancomaycin\,5.0\,\,}} = \frac{{\sum {5.3 + 5.9 + 4.7} }}{3}\\{\overline x _{vancomaycin\,5.0\,\,}} = \frac{{15.9}}{3}\, = \,5.3\end{aligned}\)

 

For the third treatment by teixobactin with 1.0 mg/kg as the dose, the colonies observed were 4 with the values 8.5, 6.0, 8.4, 6.0. Thus, 

 

\(\begin{aligned}{l}{\overline x _{teixobactin1.0\,}} = \frac{{\sum {8.5 + 6.0 + 8.4 + 6.0} }}{4}\\{\overline x _{teixobactin1.0\,}} = \frac{{28.9}}{4}\, = \,7.22\end{aligned}\)

 

For the third treatment by teixobactin with 5.0 mg/kg as the dose, the colonies observed were 4 with the values 3.8, 4.9, 5.2, 4.9. Thus,

 

\(\begin{aligned}{l}{\overline x _{teixobactin5.0\,}} = \frac{{\sum {3.8 + 4.9 + 5.2 + 4.9} }}{4}\\{\overline x _{teixobactin5.0\,}} = \frac{{18.8}}{4}\, = \,4.7\end{aligned}\)

 

Thus, the mean values of each treatment are calculated by the given formula.