Respuesta :
Answer:
mean = 10.68 m/s
standard deviation 0.3059
[/tex]\sigma_m = 0.14[/tex]
Explanation:
1) [tex]Mean = \frac{ 10.2+11+10.7+11+10.5}{5}[/tex]
mean = 10.68 m/s
2 ) standard deviation is given as
[tex]\sigma = \sqrt{ \frac{1}{N} \sum( x_i -\mu)^2}[/tex]
N = 5
[tex]\sigma =\sqrt{ \frac{1}{5} \sum{( 10.2-10.68)^2+(11-10.68)^2 + (10.7- 10.68)^2+ (11- 10.68)^2++ (10.5- 10.68)^2[/tex]
SOLVING ABOVE RELATION TO GET STANDARD DEVIATION VALUE
\sigma = 0.3059
3) ERROR ON STANDARD DEVIATION
[tex]\sigma_m = \frac{ \sigma}{\sqrt{N}}[/tex]
[tex]= \frac{0.31}{\sqrt{5}}[/tex]
[tex]\sigma_m = 0.14[/tex]
Answer:
Mean = = 10.68 m/s
Standard deviation = σ = 0.342 m/s
Error = 0.153 .
Explanation:
The data has 5 readings.
Let each of the readings be Y
Take average and find the mean X = (10.2+11+10.7+11+10.5)/5 = 53.4/5 = 10.68 m/s.
Take the difference between the data values and the mean and square them individually.
(10.2 - 10.68)² =(-0.48)² = 0.23
(11 - 10.68)² = 0.32² = 0.102
(10.7 - 10.68)² = (-0.02)² = 0.0004
(11-10.68)² =0.32² = 0.102
(10.5-10.68)² = (-0.18)² = 0.0324
Standard deviation = [tex]\sigma = \sqrt{\frac{\sum(Y-X)^2 }{n-1}}[/tex]
= [tex]\sqrt{(0.23+0.102+0.0004+0.102+0.0324)/(5-1)}[/tex]
= [tex]\sqrt{0.1167}[/tex] = 0.342 m/s
Error = Standard deviation / [tex]\sqrt{n}[/tex] = 0.342/5 = 0.153 .
