Question 1184953
What the calculation range,variance, and standard deviation of {{{7}}},{{{4}}},{{{2}}},{{{3}}},{{{4}}},{{{5}}},{{{8}}},{{{1}}},{{{9}}},{{{4}}}


Range:

The range is found by subtracting the smallest data value from the largest data value. Here, the smallest data value is {{{1}}} and the largest is {{{9}}}. Therefore, the range is:

{{{9-1=8}}}


Variance:

1. The steps that follow are also needed for finding the standard deviation. Start by writing the computational formula for the variance of a sample:


{{{s^2=(sum(x^2)-(sum(x))^2/n)/(n-1)}}}

Create a table of {{{2}}} columns and {{{11}}} rows. There will be a header row and a row for each data value. The header row should be labeled with {{{x}}} and {{{x^2}}}.
Enter the data values in the {{{x }}}column, with each data value in its own row. In the second column, put the square of each of the data values, {{{x^2}}}.
.

{{{x}}}....|....{{{x^2}}}
{{{7}}}....|....{{{49}}}
{{{4}}}....|....{{{16}}}
{{{2}}}....|....{{{4}}}
{{{3}}}....|....{{{9}}}
{{{4}}}....|....{{{16}}}
{{{5}}}....|....{{{25}}}
{{{8}}}....|....{{{64}}}
{{{1}}}....|....{{{1}}}
{{{9}}}....|....{{{81}}}
{{{4}}}....|....{{{16}}}

3. Find the sum of all the values in the first column, 


{{{sum(x)=7+4+2+3+4+5+8+1+9+4=47}}}


.{{{(sum(x))^2/n=47^2/10=2209/10=220.9 }}}

{{{sum(x^2)=49+16+4+9+16+25+64+1+81+16=281}}}

{{{s^2=(281-220.9)/(10-1)}}}

{{{s^2=60.1/9}}}

{{{s^2=6.677777777777777}}}

Standard Deviation

{{{s=sqrt(6.677777777777777)}}}

{{{s=2.584139659108574}}}



Answer:

Range: {{{8}}}

Variance: {{{6.67777777777777}}}

Standard deviation: {{{2.584139659108574}}}