After every score in a sample is multiplied by 3, the mean is calculated and found to be M = 21. What was the mean for the original scores?

To find the original mean before the scores were multiplied by 3, we can use the following steps:

1. Let the original mean be denoted by $\mu$.
2. According to the problem, after every score in the sample is multiplied by 3, the new mean is calculated to be $M = 21$.
3. When each score in a sample is multiplied by a constant, the mean of the sample is also multiplied by that constant. Therefore, the new mean $M$ is 3 times the original mean $\mu$.

Mathematically, this can be expressed as: $M = 3 \mu$

4. We know that $M = 21$. So, we can set up the equation: $21 = 3 \mu$

5. To find the original mean $\mu$, we solve for $\mu$ by dividing both sides of the equation by 3: $\mu = \frac{21}{3}$

6. Simplifying the right-hand side, we get: $\mu = 7$

Therefore, the mean for the original scores was 7.