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The mean of a sequence of numbers is the average.
The true statement is: [tex]\mathbf{mn = m_1 \times n_1 + m_2 \times n_2}[/tex]
The given parameters are:
[tex]\mathbf{Mean = m}[/tex]
[tex]\mathbf{Size = n}[/tex]
The mean of a dataset is calculated as:
[tex]\mathbf{Mean = \frac{\sum x}{Size}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{\sum x}{n}}[/tex]
Multiply both sides by m
[tex]\mathbf{\sum x = mn}[/tex]
When the sequence is split into two, we have:
[tex]\mathbf{\sum x_1 = m_1\times n_1}[/tex]
[tex]\mathbf{\sum x_2 = m_2\times n_2}[/tex]
Where:
[tex]\mathbf{\sum x_ = \sum x_1 + \sum x_2}[/tex]
So, we have:
[tex]\mathbf{mn = m_1 \times n_1 + m_2 \times n_2}[/tex]
Hence, the true statement is: [tex]\mathbf{mn = m_1 \times n_1 + m_2 \times n_2}[/tex]
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