Chapter 3
Numerically
Summarizing Data
Insert photo of
cover
Section 3.3 Measures of Central Tendency and
Dispersion from Grouped Data
Objectives
1. Approximate the mean of a variable from grouped
data
2. Compute the weighted mean
3. Approximate the variance and standard deviation of
a variable from grouped data
Objective 1
• Approximate the Mean of a Variable from
Grouped Data
EXAMPLE Approximating the Mean from a Relative
Frequency Distribution
The National Survey of Student Engagement is a survey that (among other
things) asked first year students at liberal arts colleges how much time they
spend preparing for class each week. The results from the 2007 survey are
summarized below. Approximate the mean number of hours spent
preparing for class each week.
Hours
0
1-5
6-10
11-15
16-20
21-25
26-30
31-35
Frequency
0
130
250
230
180
100
60
50
Source:http://nsse.iub.edu/NSSE_2007_Annual_Report/docs/withhold/NSSE_2007_Annual_Report.pdf
Time
Frequency
xi
x i fi
0
0
0
0
1-5
130
3.5
455
6 - 10
250
8.5
2125
11 - 14
230
13.5
3105
16 - 20
180
18.5
3330
21 - 25
100
23.5
2350
26 – 30
60
28.5
1710
31 – 35
50
33.5
1675
f
i
x f
 1000
x
i i
x f
f
i i
i
14, 750
1000
 14.75

 14,750
Objective 2
• Compute the Weighted Mean
EXAMPLE Computed a Weighted Mean
Bob goes the “Buy the Weigh” Nut store and creates his
own bridge mix. He combines 1 pound of raisins, 2
pounds of chocolate covered peanuts, and 1.5 pounds
of cashews. The raisins cost $1.25 per pound, the
chocolate covered peanuts cost $3.25 per pound, and
the cashews cost $5.40 per pound. What is the cost per
pound of this mix.
1($1.25)  2($3.25)  1.5($5.40)
1  2  1.5
$15.85

4.5
 $3.52
xw 
Objective 3
• Approximate the Variance and Standard
Deviation of a Variable from Grouped Data
EXAMPLE Approximating the Mean from a Relative
Frequency Distribution
The National Survey of Student Engagement is a survey that (among other
things) asked first year students at liberal arts colleges how much time they
spend preparing for class each week. The results from the 2007 survey are
summarized below. Approximate the variance and standard deviation
number of hours spent preparing for class each week.
Hours
0
1-5
6-10
11-15
16-20
21-25
26-30
31-35
Frequency
0
130
250
230
180
100
60
50
Source:http://nsse.iub.edu/NSSE_2007_Annual_Report/docs/withhold/NSSE_2007_Annual_Report.pdf
Time
Frequency
0
0
1-5
 x  x
i
2
fi
130
x
0
3.5
0
16453.13
6 - 10
250
8.5
9765.625
11 - 14
230
13.5
359.375
16 - 20
180
18.5
2531.25
21 - 25
100
23.5
7656.25
26 - 30
60
28.5
11343.75
31 - 35
50
33.5
17578.13
 fi  1000
x  x f



 f  1
 x  x
2
i
fi  65,687.5
2
s
2
i
i
s  s2
i
65, 687.5

1000  1
 65.8
65, 687.5
999
 8.1 hours
