1. What is Combined Mean?

The combined mean (also known as weighted average mean) is the overall mean of two or more groups when combined together. It takes into account both the means and the sample sizes of the individual groups.

2. How Does the Calculator Work?

The calculator uses the combined mean formula:

Where:

• \( n_1 \) — Sample size of group 1
• \( \mu_1 \) — Mean of group 1
• \( n_2 \) — Sample size of group 2
• \( \mu_2 \) — Mean of group 2

Explanation: The formula calculates a weighted average where larger sample sizes have greater influence on the final combined mean.

3. Importance of Combined Mean Calculation

Details: Combined mean is essential in statistics for merging data from different groups, analyzing pooled data in meta-analyses, and understanding overall trends when dealing with multiple datasets.

4. Using the Calculator

Tips: Enter positive sample sizes (n1, n2) and their corresponding means (μ1, μ2). The calculator will compute the weighted average mean of the two groups.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between combined mean and simple average?
A: Combined mean weights each group by its sample size, while simple average treats all groups equally regardless of size.

Q2: Can this formula be extended to more than two groups?
A: Yes, for k groups: \( \text{Combined Mean} = \frac{\sum_{i=1}^k n_i \mu_i}{\sum_{i=1}^k n_i} \)

Q3: When should I use combined mean vs weighted mean?
A: Combined mean is specifically for combining groups with different sample sizes, while weighted mean can use any weights (not just sample sizes).

Q4: What if my sample sizes are very different?
A: The group with larger sample size will have greater influence on the combined mean, which is mathematically appropriate.

Q5: Can this be used for proportions as well as means?
A: Yes, the same formula works for combining proportions from different groups.