Question

suppose that you made four measurement of a speed of a rocket: 12.7 km/s, 13.4 km/s, 12.6 km, and 13.3 km/s. compute: the mean, the standard deviations, and the standard deviation of the mean

Answer 1

Answer:

Mean = 13 kilometer per second

Standard Deviation = 0.4082 kilometer per second

Step-by-step explanation:

We are given the following data set of rocket speed in kilometer per second in the question:

12.7, 13.4, 12.6, 13.3

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{52}{4} = 13$

Deviations from mean = -0.3, 0.4, -0.4, 0.3

Sum of squares of differences =

0.09 + 0.16 + 0.16 + 0.09 = 0.5

$S.D = \sqrt{\dfrac{0.5}{3}} = 0.4082$

Mean = 13 kilometer per second

Standard Deviation = 0.4082 kilometer per second