Question

Suppose you made 5 measurements of the speed of a rocket:10.2 m/s, 11.0 m/s, 10.7 m/s, 11.0 m/s and 10.5 m/s. From these measurements you conclude the rocket is traveling at a constant speed. Calculate the mean, standard deviation, and error on the mean.

Answer 1

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 = $\sigma = \sqrt{\frac{\sum(Y-X)^2 }{n-1}}$

                                = $\sqrt{(0.23+0.102+0.0004+0.102+0.0324)/(5-1)}$

                                 = $\sqrt{0.1167}$ = 0.342 m/s

Error = Standard deviation / $\sqrt{n}$ = 0.342/5 = 0.153 .

Answer 2

Answer:

mean = 10.68 m/s

standard deviation 0.3059

[/tex]\sigma_m = 0.14[/tex]  

Explanation:

1) $Mean = \frac{ 10.2+11+10.7+11+10.5}{5}$

  mean = 10.68 m/s

2 ) standard deviation is given as

$\sigma = \sqrt{ \frac{1}{N} \sum( x_i -\mu)^2}$

N = 5

   $\sigma =\sqrt{ \frac{1}{5} \sum{( 10.2-10.68)^2+(11-10.68)^2 + (10.7- 10.68)^2+ (11- 10.68)^2++ (10.5- 10.68)^2$

SOLVING ABOVE RELATION TO GET STANDARD DEVIATION VALUE

\sigma  = 0.3059

3) ERROR ON STANDARD DEVIATION

$\sigma_m = \frac{ \sigma}{\sqrt{N}}$

               $= \frac{0.31}{\sqrt{5}}$

$\sigma_m = 0.14$