6 parts of 1 point are reported on a log scale and are provided in the table. Note that a decrease of 1.0 on this scale reflects a 10-fold decrease in MRSA abundance.
Answer (2)
Calculate the mean log of number of colonies for Control: M e a n C o n t ro l = 4 9.0 + 9.5 + 9.0 + 8.9 = 9.1
Calculate the mean log of number of colonies for Vancomycin (1.0 mg/kg): M e a n Van co m yc in 1.0 = 3 8.5 + 8.4 + 8.2 ≈ 8.37
Calculate the mean log of number of colonies for Vancomycin (5.0 mg/kg): M e a n Van co m yc in 5.0 = 3 5.3 + 5.9 + 4.7 = 5.3
Calculate the mean log of number of colonies for Teixobactin (1.0 mg/kg): M e a n T e i x o ba c t in 1.0 = 4 8.5 + 6.0 + 8.4 + 6.0 = 7.225
Calculate the mean log of number of colonies for Teixobactin (5.0 mg/kg): M e a n T e i x o ba c t in 5.0 = 4 3.8 + 4.9 + 5.2 + 4.9 = 4.7
The means are: Control: 9.1 , Vancomycin (1.0 mg/kg): 8.37 , Vancomycin (5.0 mg/kg): 5.3 , Teixobactin (1.0 mg/kg): 7.225 , Teixobactin (5.0 mg/kg): 4.7
Explanation
Understanding the Problem We are given a table with data about different treatments (Control, Vancomycin, and Teixobactin) and their effect on MRSA abundance, measured as the log of the number of colonies. The goal is to calculate the mean log of the number of colonies for each treatment and dose.
Calculating the Mean for Control For the Control treatment, the log of the number of colonies are 9.0, 9.5, 9.0, and 8.9. To find the mean, we add these values and divide by the number of values, which is 4. M e a n C o n t ro l = 4 9.0 + 9.5 + 9.0 + 8.9 = 4 36.4 = 9.1
Calculating the Mean for Vancomycin (1.0 mg/kg) For Vancomycin at a dose of 1.0 mg/kg, the log of the number of colonies are 8.5, 8.4, and 8.2. We calculate the mean by adding these values and dividing by 3. M e a n Van co m yc in 1.0 = 3 8.5 + 8.4 + 8.2 = 3 25.1 ≈ 8.37
Calculating the Mean for Vancomycin (5.0 mg/kg) For Vancomycin at a dose of 5.0 mg/kg, the log of the number of colonies are 5.3, 5.9, and 4.7. We calculate the mean by adding these values and dividing by 3. M e a n Van co m yc in 5.0 = 3 5.3 + 5.9 + 4.7 = 3 15.9 = 5.3
Calculating the Mean for Teixobactin (1.0 mg/kg) For Teixobactin at a dose of 1.0 mg/kg, the log of the number of colonies are 8.5, 6.0, 8.4, and 6.0. We calculate the mean by adding these values and dividing by 4. M e a n T e i x o ba c t in 1.0 = 4 8.5 + 6.0 + 8.4 + 6.0 = 4 28.9 = 7.225
Calculating the Mean for Teixobactin (5.0 mg/kg) For Teixobactin at a dose of 5.0 mg/kg, the log of the number of colonies are 3.8, 4.9, 5.2, and 4.9. We calculate the mean by adding these values and dividing by 4. M e a n T e i x o ba c t in 5.0 = 4 3.8 + 4.9 + 5.2 + 4.9 = 4 18.8 = 4.7
Final Results The means for each treatment and dose are:
Control: 9.1
Vancomycin (1.0 mg/kg): 8.37
Vancomycin (5.0 mg/kg): 5.3
Teixobactin (1.0 mg/kg): 7.225
Teixobactin (5.0 mg/kg): 4.7
Examples
Understanding the mean effect of different treatments is crucial in medicine and biology. For instance, when testing new drugs, calculating the average response helps determine the drug's effectiveness. This is similar to calculating the mean log of colonies in our problem, where we assess how well each treatment reduces bacterial abundance. By comparing these means, scientists can identify the most effective treatments and optimize dosages for better outcomes. This statistical approach ensures decisions are based on solid evidence, improving healthcare and treatment strategies.
We calculated the mean log of MRSA colonies for various treatments, finding means of 9.1 for Control, 8.37 for Vancomycin (1.0 mg/kg), 5.3 for Vancomycin (5.0 mg/kg), 7.225 for Teixobactin (1.0 mg/kg), and 4.7 for Teixobactin (5.0 mg/kg). The results show varying effectiveness in reducing MRSA abundance. This data provides insight into the treatments' potency against bacteria.
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