Standard Deviation and
Variance (Class 2)
OBJ: • Find range, measures of
central tendency, and construct
tables and graphs
Below are the algebra test scores
for a class of 25 students:
56 57 58 60 61 65 67 68 70 71 74 75 77
79 82 87 88 89 92 95 96 97 98 99 99
Calculator commands: (at the
bottom of the second page of notes)
• STAT, 1 (for EDIT), 50,ENTER (repeat
for all data), STAT,  (for CALC), 1
(for 1-VAR STAT), ENTER (To clear
data,▲L1, CLEAR, ENTER)
• 2ND STAT (for LIST),  (for
MATH), 8, (for VARIANCE), 2ND 1
(for L1)
Give the mean, median, and
mode
Mean
78.4
Median
77
Mode
99
Give the standard deviation and
variance
Standard deviation
14.8
Variance
218.1
Below are the algebra test scores
for a class of 25 students:
50 64 68 70 70 72 73 75 75 76 78 78 79
80 81 82 82 82 85 88 88 89 90 92 93
Below are the algebra test scores
for a class of 25 students:
56 57 58 60 61 65 67 68 70 71 74 75 77
79 82 87 88 89 92 95 96 97 98 99 99
Give the mean, median, and mode. Give
the standard deviation and variance
Class 1
Class 2
Mean
78.4
Median
79
Mode
82
Standard deviation
9.8
Variance
95.2
Mean
78.4
Median
77
Mode
99
Standard deviation
14.8
Variance
218.1
Give range and class width
Range
99-56
43
Class Width
43
6
7 1/6 →
8
Construct a frequency table and a
cumulative frequency table with 6 classes
Class
Relative
5 5 5 6 6 6 6 67 7 7 7 7
Frequency 6 7 8 0 1 5 7 8 0 1 4 5 7
7 8 8 8 8 9 9 99 9 9 9
9 2 7 8 9 2 5 67 8 9 9
Construct a frequency table and a
cumulative frequency table with 6 classes
Class
Relative
Frequency
Class
Relative
Frequency
56-63
5
64-71
5
72-79
4
80-87
2
88-95
4
96-103
5
Construct a frequency table and a
cumulative frequency table with 6 classes
Cumulative
Class
< 56
Frequency
#
0
%
0
Class
Relative
Frequency
56-63
5
64-71
5
72-79
4
80-87
2
88-95
4
96-103
5
Construct a frequency table and a
cumulative frequency table with 6 classes
Class
56-63
Relative Cumulative Frequency
Frequency Class
#
%
< 56
0
0%
5
< 64
5
20 %
64-71
5
< 72
10
40 %
72-79
4
<80
14
56 %
80-87
2
< 88
16
64 %
88-95
4
< 96
20
80 %
Construct a histogram. Clearly mark
axes.
Class
56-63
64-71
72-79
80-87
88-95
96-103
Relative
F
Frequency r
e
5
q
5
u
4
e
2
n
4
c
5
y
25
Test Scores
Go to frequency polygon at the top of
the next page of notes.
Give all class marks.
56 + 63
2
59.5
64 + 71
2
67.5
59.5
67.5
75.5
83.5
91.5
99.5
Construct a frequency polygon, mark
axes
F
Class
Relative
r
Mark 51.5 Frequency
e
59.5
5
q
u
67.5
5
e
75.5
4
n
83.5
2
c
91.5
4
y
99.5
5
107.5
25
Test Scores
Construct an ogive. Clearly mark both
axes
Cumulative
Class
Frequency
#
%
< 56
0
0%
< 64
5
20 %
< 72
10
40 %
<80
14
56 %
< 88
16
64 %
< 96
20
80 %
< 104
25
100%
R
e
l
a
t
i
v
e
C
u
m
u
l
a
t
i
v
e
F
r
e
q
u
e
n
c
y
Test Scores