Find the mean,variance,and standard deviation of the uniform distribution over the interval [0,26] without using integration.
A) expected value (mean): 13 Variance: 56.333 Standard deviation: 7.506
B) expected value (mean): 56.333 Variance: 13 Standard deviation: 7.506
C) expected value (mean): 56.333 Variance: 7.506 Standard deviation: 13
D) expected value (mean): 7.506 Variance: 13 Standard deviation: 56.333
E) expected value (mean): 13 Variance: 7.506 Standard deviation: 56.333

Question

​Find the mean,variance,and standard deviation of the uniform distribution  over the interval [0,26] without using integration. ​
A) ​expected value (mean): 13 Variance: 56.333 Standard deviation: 7.506 ​ 
B) ​expected value (mean): 56.333 Variance: 13 Standard deviation: 7.506 ​ 
C) ​expected value (mean): 56.333 Variance: 7.506 Standard deviation: 13 ​ 
D) ​expected value (mean): 7.506 Variance: 13 Standard deviation: 56.333 
E) ​expected value (mean): 13 Variance: 7.506 Standard deviation: 56.333

Quizplus · Accepted Answer

For a uniform distribution over the interval [a,b], the mean is given by (a+b)/2 and the variance is ((b-a)^2)/12. Therefore, for the uniform distribution over [0,26], we have:
- Mean = (0+26)/2 = 13
- Variance = ((26-0)^2)/12 = 676/12 = 56.333
- Standard deviation = sqrt(variance) = sqrt(56.333) = 7.506. 
Therefore, choice A is the correct answer.

​Find the Mean,variance,and Standard Deviation of the Uniform Distribution

Find the Mean,variance,and Standard Deviation of the Uniform Distribution