Question

1. a population of $n = 7$ scores has a mean of $mu = 13$. what is the value of $sigma x$ for this population?
2. one sample of $n = 10$ scores has a mean of 8, and a second sample of $n = 5$ scores has a mean of 2. if the two samples are combined, what is the mean for the combined sample?

Explanation:

Step1: Recall the mean formula

The formula for the population mean $\mu=\frac{\sum X}{N}$. We are given $N = 7$ and $\mu=13$.

Step2: Solve for $\sum X$

Rearranging the formula $\sum X=\mu\times N$. Substituting the given values, we get $\sum X = 13\times7=91$.

Step3: For the second - part, find the sum of scores in each sample

For the first sample with $n_1 = 10$ and $\bar{x}_1=8$, the sum of scores $\sum X_1=n_1\bar{x}_1=10\times8 = 80$. For the second sample with $n_2 = 5$ and $\bar{x}_2=2$, the sum of scores $\sum X_2=n_2\bar{x}_2=5\times2=10$.

Step4: Find the combined sum and combined sample size

The combined sum of scores $\sum X_{combined}=\sum X_1+\sum X_2=80 + 10=90$. The combined sample size $n_{combined}=n_1 + n_2=10 + 5=15$.

Step5: Calculate the combined mean

The combined mean $\bar{x}_{combined}=\frac{\sum X_{combined}}{n_{combined}}=\frac{90}{15}=6$.

Answer:

For question 9: 91
For question 10: 6