Question

1. a sample of n = 5 scores has a mean of m = 12. if one new score with a value of x = 17 is added to the sample, then what is the mean for the new sample?

Explanation:

Step1: Find the sum of the original sample

The formula for the mean $M=\frac{\sum X}{n}$. Given $n = 5$ and $M = 12$, we can find the sum of the original scores $\sum X_{old}$. Rearranging the formula gives $\sum X_{old}=M\times n$. So, $\sum X_{old}=12\times5 = 60$.

Step2: Find the sum of the new sample

A new score $X = 17$ is added. So the sum of the new sample $\sum X_{new}=\sum X_{old}+17$. Substituting the value of $\sum X_{old}$, we get $\sum X_{new}=60 + 17=77$.

Step3: Find the new sample size

The original sample size was $n = 5$, and one new score is added. So the new sample size $n_{new}=5 + 1=6$.

Step4: Calculate the new mean

Using the mean formula $M_{new}=\frac{\sum X_{new}}{n_{new}}$. Substituting $\sum X_{new}=77$ and $n_{new}=6$, we get $M_{new}=\frac{77}{6}\approx12.83$.

Answer:

$\frac{77}{6}\approx12.83$