Question

A certain treatment is used in two different centers, A and B; patients in center A were 25 and were on average 54 years old; patients treated in center B were 62 and had mean age equal to 58 years. What is the overall mean among all patients who got the treatment?​

Answer 1

The overall mean age among all patients who received the treatment at both centers A and B is calculated using a weighted average, yielding an overall mean age of approximately 56.85 years.

Step-by-step explanation:

To calculate the overall mean age of patients who got the treatment at both centers, A and B, we need to use a weighted average. The mean age for patients in center A is 54 years, and there are 25 patients. The mean age for patients in center B is 58 years, and there are 62 patients. The weighted average can be calculated as follows:

1. Multiply the mean age of patients in each center by the number of patients in that center.
2. Add the results from step 1 together to get the total sum of ages for all patients.
3. Divide the total sum of ages by the total number of patients to find the overall mean age.

Applying these steps:

(54 * 25) + (58 * 62) = 1,350 + 3,596 = 4,946 total years

Total number of patients = 25 + 62 = 87

Overall mean age = 4,946 / 87 ≈ 56.85 years

Thus, the overall mean age among all patients who got the treatment at both centers is approximately 56.85 years.