24 12 pt Use the table of listed data below to find the samp

24, (12 pt) Use the table of listed data below to find the sample mean x, the sum of squares SS and sample standard deviation s of the data: (label each clearly)

Solution

The table that is filled seems absolutely correct.

Let us understand what each term means:

x_i = Variable value

f_i = frequency of number of times that value appears

Mean or the average is given by

summation of ( x_if_i ) / total observations

= summation of ( x_if_i ) / summation of (f_i )

In your case the data can be discretely written as:

{ 3,,3,,3,,3,,5,,5,,5,,5,,5,,5,,7,,7,,7,,9,,9,,11,,11,,11,,11,,11,,11} whose mean = sum of all values / no. of values

And that is what is done:

So, we get the mean or the average as : 136 / 20 = 6.8 ( we call it x-bar)

Now, to calculate Variance / Standard Deviation :.

Std.Dev in a data set = square root of [ sum of squares of deviations / n-1 ]

Deviations are deviations from mean :

Thus, we get the (x - xbar) [e.g 3 - 6.8 = -3.8 ] which is the deviation

We need the squares of these deviations, and thus get column 4

Column 5 :

Each square term is multiplied with it\'s frequency since, the values and so also the deviations are repeated that many number of times.

SS = sum of square terms, that is all the terms in the last column.

To calculate the sample standard deviation, we dvide it by n-1 and take the square root. That is our Std.Dev.

Hope this explains what you are looking for. Ask if you need more explanation