Answer to Question #318057 in Statistics and Probability for Niu_bi

Question

Mean and Variance of Sampling Method:

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

Answer 1

1.$\sum x^2=2500+2116+2601+2025+1600+1849+3249+3364+4096+3481+3600+3844=34325$

2.

$\sum x=50+46+51+45+40+43+57+58+64+59+60+62=636$

3. $\mu=(100+95+98+97+93+92+91+96+99+89)/10=950/10=95$

$\sum (x-\mu)^2=25+0+9+4+4+9+16+1+16+36=120$

4. $\sigma^2=\frac{ \sum (x-\mu)^2}{n-1}=120/9=13.3$

5. $\sigma=\sqrt{\sigma^2}=3.65$

6. $​ \sum (x-\mu)^2=9+49+4+64+169+100+16+25+121+36+49+81 ​ =723$