Question

the equation shown is used in statistics to relate z, the z - score of a data element, to x, the value of the data element, m, the mean of the data set, and d, the standard deviation of the data:
$z = \frac{x - m}{d}$
solve the formula for m, the mean of the data set.
enter your answer in the box.
$m = \square$

Explanation:

Step1: Multiply both sides by \( d \)

To eliminate the denominator \( d \) on the right - hand side, we multiply both sides of the equation \( z=\frac{x - m}{d} \) by \( d \). Using the multiplication property of equality (if \( a = b \), then \( a\times c=b\times c \) for any real number \( c \)), we get:
\( z\times d=\frac{x - m}{d}\times d \)
Simplifying both sides, the right - hand side \( \frac{x - m}{d}\times d=x - m \), and the left - hand side is \( zd \). So the equation becomes \( zd=x - m \).

Step2: Solve for \( m \)

We want to isolate \( m \). We can rewrite the equation \( zd=x - m \) as \( x - m=zd \) (by the symmetric property of equality, if \( a = b \), then \( b = a \)). Then, we subtract \( x \) from both sides and multiply by - 1 (or we can add \( m \) to both sides and subtract \( zd \) from both sides). Let's add \( m \) to both sides: \( x - m+m=zd + m \), which simplifies to \( x=zd + m \). Then, subtract \( zd \) from both sides: \( x-zd=zd + m-zd \). Simplifying the right - hand side, \( zd-zd = 0 \), so we get \( m=x - zd \).

Answer:

\( x - zd \)