SOLUTION: Hi, I am stuck on another one of these problems, can someone help me? Estimate the population standard deviation of the grouped data. Score Frequency 1-3 1

Score       Frequency
 1-3           1 
 4-6           6 
 7-9           3 

 a. √6.0
 b. √5.6
 c. √3.24
 d. √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=Sf=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=Sf=10    Sf*x=56

Divide the Sf*x by n, or  = 5.6 = m

Make a column for x-m

Score  Midpoint=x  Frequency   f*x   x-m
 1--3      2         1          2   -3.6
 4--6      5         6         30   - .6
 7--9      8         3         24    2.4
-----------------------------------------
               n=Sf=10    Sf*x=56

Make a column for (x-m)sup>2

Score  Midpoint=x  Frequency   f*x   x-m  (x-m)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=Sf=10    Sf*x=56 

Make a column for f*(x-m)sup>2 and add it up:

Score  Midpoint=x  Frequency   f*x   x-m  (x-m)²          f*(x-m)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=Sf=10    Sf*x=56               Sf*(x-m)² = 32.4


Divide Sf*(x-m)² by n



. That's choice c.

Edwin