document.write( "Question 1190485: -5
\n" ); document.write( "3
\n" ); document.write( "-5
\n" ); document.write( "-5
\n" ); document.write( "-3
\n" ); document.write( "-3
\n" ); document.write( "-3\r
\n" ); document.write( "\n" ); document.write( "Calculate the value of the sample variance. \n" ); document.write( "
Algebra.Com's Answer #822215 by math_tutor2020(3835)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "First we add up all the values
\n" ); document.write( "(-5)+(3)+(-5)+(-5)+(-3)+(-3)+(-3) = -21\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Then divide by n = 7 because there are 7 items in this list
\n" ); document.write( "-21/n = -21/7 = -3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The sample mean is xbar = -3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Next, we subtract xbar from each item
\n" ); document.write( "-5 - xbar = -5 - (-3) = -2
\n" ); document.write( "3 - xbar = 3 - (-3) = 6
\n" ); document.write( "-5 - xbar = -5 - (-3) = -2
\n" ); document.write( "-5 - xbar = -5 - (-3) = -2
\n" ); document.write( "-3 - xbar = -3 - (-3) = 0
\n" ); document.write( "-3 - xbar = -3 - (-3) = 0
\n" ); document.write( "-3 - xbar = -3 - (-3) = 0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Perhaps it's better to use a table to organize the data values\n" ); document.write( "\n" ); document.write( "
xx-xbar
-5-2
36
-5-2
-5-2
-30
-30
-30
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The next step is to square each item in the second column to form the column (x-xbar)^2\n" ); document.write( "\n" ); document.write( "
xx-xbar(x-xbar)^2
-5-24
3636
-5-24
-5-24
-300
-300
-300
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Add up everything in the third column:
\n" ); document.write( "4+36+4+4+0+0+0 = 48\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Then divide by n-1 = 7-1 = 6 to compute the sample variance
\n" ); document.write( "48/(n-1) = 48/6 = 8\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Such a process is fairly tedious busywork if you are dealing with large data sets.
\n" ); document.write( "I recommend using a calculator such as this one
\n" ); document.write( "https://www.calculatorsoup.com/calculators/statistics/variance-calculator.php
\n" ); document.write( "and this is a handy tool to check your work.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To compute the standard deviation, you apply the square root to the variance
\n" ); document.write( "Standard Deviation = sqrt(variance)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer: 8
\n" ); document.write( " \n" ); document.write( "
\n" );