Answer to Question #318055 in Statistics and Probability for Niu_bi

Question

Mean and Variance of

Sampling Method:

1. What is the mean if the given are the following: 50, 46, 51, 45, 40, 43, 57, 58, 64, 59, 60, 62?
2. What is the variance if the given are the following: 50, 46, 51, 45, 40, 43, 57, 58, 64, 59, 60, 62?
3. What is the summation of x if the given are the following: 100; 95; 98; 97; 93; 92; 91; 96; 99; 89?
4. What is the mean if the given are the following: 100; 95; 98; 97; 93; 92; 91; 96; 99; 89?
5. What is the summation of x squared if the given are the following: 100; 95; 98; 97; 93; 92; 91; 96; 99; 89? ∑𝑥²?
6. What is the standard deviation if the given are the following: 50, 46, 51, 45, 40, 43, 57, 58, 64, 59, 60, 62?

Answer 1

1. $\mu=(50+46+51+45+40+43+57+58+64+59+60+62)/12=53$

2. $\sigma^2=\frac{\sum (x-\mu)^2}{n-1}=\frac{9+49+4+64+169+100+16+25+121+36+49+81}{11}=65.6$

3.$\sum (x)=100+95+98+97+93+92+91+96+99+89=950$

4. $\mu=950/10=95$

5.$\sum x^2=10000+9025+9604+8281+8649+8464+8281+8216+9801+7921=88242$

6.$\sigma=\sqrt{\sigma^2}=\sqrt{65.6}=8.1$