Question

The following six independent length measurements were made (in feet) for a line: 736.352, 736.363, 736.375, 736.324, 736.358, and 736.383. Determine the most probable value.

Answer 1

Answer:

a) $\bar X =\frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359$

b) The sample deviation is calculated from the following formula:

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And for this case after replace the values and with the sample mean already calculated we got:

$s= 0.0206$

If we assume that the data represent a population then the standard deviation would be given by:

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}$

And then the deviation would be:

$\sigma=0.0188$

Step-by-step explanation:

For this case we have the following dataset:

736.352, 736.363, 736.375, 736.324, 736.358, and 736.383

Part a: Determine the most probable value.

For this case the most probably value would be the sample mean given by this formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

And if we replace we got:

$\bar X =\frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359$

Part b: Determine the standard deviation

The sample deviation is calculated from the following formula:

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And for this case after replace the values and with the sample mean already calculated we got:

$s= 0.0206$

If we assume that the data represent a population then the standard deviation would be given by:

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}$

And then the deviation would be:

$\sigma=0.0188$