Post on 04-Jan-2016
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 thebottom 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
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
Class
Relative
Frequency
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
Class
Relative
Frequency
56-63 5
64-71 5
72-79 4
80-87 2
88-95 4
96-103 5
Cumulative Frequency
Class
< 56
# %
0 0
Construct a frequency table and a cumulative frequency table with 6 classes
Class
Relative
Frequency
56-63 5
64-71 5
72-79 4
80-87 2
88-95 4
96-103 5
Cumulative
ClassFrequency
# %
< 56 0 0 %
< 64 5 20 %
< 72 10 40 %
<80 14 56 %
< 88 16 64 %
< 96 20 80 %
< 104 25 100%
Construct a histogram. Clearly mark axes.
F
r
e
q
u
e
n
c
y
Test Scores
Class Relative
Frequency
56-63 5
64-71 5
72-79 4
80-87 2
88-95 4
96-103 5
25
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
Frequency
Test Scores
Class
Mark 51.5
Relative
Frequency
59.5 5
67.5 5
75.5 4
83.5 2
91.5 4
99.5 5
107.5 25
Construct an ogive. Clearly mark both axes
R C F e u r l m ea u qt l ui a ev t ne i c v y e
Test Scores
Cumulative
ClassFrequency
# %
< 56 0 0 %
< 64 5 20 %
< 72 10 40 %
<80 14 56 %
< 88 16 64 %
< 96 20 80 %
< 104 25 100%