Question 148187
Hi, I am stuck on another one of these problems, can someone help me?

Estimate the population standard deviation of the grouped data. 
<pre><font siZe = 3 color = "indigo"><b>
Score       Frequency
 1-3           1 
 4-6           6 
 7-9           3 

 a. &#8730;6.0
 b. &#8730;5.6
 c. &#8730;3.24
 d. &#8730;4.24

Make a column for the Midpoint of each class, by
averaging the lower and upper limit of each
score:

Score  Midpoint=x  Frequency=f   
 1--3     2          1 
 4--6     5          6 
 7--9     8          3 

Add up the Frequencies:

Score  Midpoint=x  Frequency=f   
 1--3      2         1 
 4--6      5         6 
 7--9      8         3
-----------------------------------------
               n=<font face = "symbol">S</font>f=10

Make a column for f*x,and add that column:



Score  Midpoint=x  Frequency   f*x
 1--3      2         1          2 
 4--6      5         6         30
 7--9      8         3         24
----------------------------------
               n=<font face = "symbol">S</font>f=10    <font face = "symbol">S</font>f*x=56

Divide the <font face = "symbol">S</font>f*x by n, or {{{56/10}}} = 5.6 = <font face = "symbol">m</font>

Make a column for x-<font face = "symbol">m</font>

Score  Midpoint=x  Frequency   f*x   x-<font face = "symbol">m</font>
 1--3      2         1          2   -3.6
 4--6      5         6         30   - .6
 7--9      8         3         24    2.4
-----------------------------------------
               n=<font face = "symbol">S</font>f=10    <font face = "symbol">S</font>f*x=56

Make a column for (x-<font face = "symbol">m</font>)sup>2</sup>

Score  Midpoint=x  Frequency   f*x   x-<font face = "symbol">m</font>  (x-<font face = "symbol">m</font>)²
 1--3      2         1          2   -3.6  12.96 
 4--6      5         6         30   - .6    .36
 7--9      8         3         24    2.4   5.76
------------------------------------------------
               n=<font face = "symbol">S</font>f=10    <font face = "symbol">S</font>f*x=56 

Make a column for f*(x-<font face = "symbol">m</font>)sup>2</sup> and add it up:

Score  Midpoint=x  Frequency   f*x   x-<font face = "symbol">m</font>  (x-<font face = "symbol">m</font>)²          f*(x-<font face = "symbol">m</font>)²
 1--3      2         1          2   -3.6  12.96             12.96
 4--6      5         6         30   - .6    .36              2.16
 7--9      8         3         24    2.4   5.76             17.28
-----------------------------------------------------------------
               n=<font face = "symbol">S</font>f=10    <font face = "symbol">S</font>f*x=56               <font face = "symbol">S</font>f*(x-m)² = 32.4


Divide <font face = "symbol">S</font>f*(x-<font face = "symbol">m</font>)² by n

{{{sigma^2 = SIGMA(f*(x-mu)^2)/n = 32.4/10 = 3.24}}}

{{{sigma = sqrt(3.24)}}}. That's choice c.

Edwin</pre>