Question

The mean of a sequence of n numbers is m. If we split the sequence into two sequences of lengths n1 and n2 and compute their means m1 and m2, which of the following is TRUE?

Answer 1

The mean of a sequence of numbers is the average.

The true statement is: $\mathbf{mn = m_1 \times n_1 + m_2 \times n_2}$

The given parameters are:

$\mathbf{Mean = m}$

$\mathbf{Size = n}$

The mean of a dataset is calculated as:

$\mathbf{Mean = \frac{\sum x}{Size}}$

So, we have:

$\mathbf{m = \frac{\sum x}{n}}$

Multiply both sides by m

$\mathbf{\sum x = mn}$

When the sequence is split into two, we have:

$\mathbf{\sum x_1 = m_1\times n_1}$

$\mathbf{\sum x_2 = m_2\times n_2}$

Where:

$\mathbf{\sum x_ = \sum x_1 + \sum x_2}$

So, we have:

$\mathbf{mn = m_1 \times n_1 + m_2 \times n_2}$

Hence, the true statement is: $\mathbf{mn = m_1 \times n_1 + m_2 \times n_2}$

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