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
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