Question

What is an example of when you would want consistent data and, therefore, a small standard deviation?

Answer 1

Answer:

12.1, 12.3,12.4,12.5,12.3,12.1,12.2

$\bar X= \frac{12.1+12.3+12.4+12.5+12.3+12.1+12.2}{7}=12.271$

And for the standard deviation we can use the following formula:

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

And after replace we got:

$s = 0.1496$

And as we can ee we got a small value for the deviation <1 on this case.

Step-by-step explanation:

For example if we have the following data:

12.1, 12.3,12.4,12.5,12.3,12.1,12.2

We see that the data are similar for all the observations so we would expect a small standard deviation

If we calculate the sample mean we can use the following formula:

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

And replacing we got:

$\bar X= \frac{12.1+12.3+12.4+12.5+12.3+12.1+12.2}{7}=12.271$

And for the standard deviation we can use the following formula:

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

And after replace we got:

$s = 0.1496$

And as we can ee we got a small value for the deviation <1 on this case.