Grade percentages for this class
Analyze the Data by:
Finding the:
1. Mean
2. Median
3. Mode
4. Range
5. Outliers
6. Draw a box and
whisker plot
7. Your percentile rank
99
82
80
65
89
71
47
80
74
78
87
78
91
71
95
91
91
73
70
94
63
49
79
79
74
65
88
21
47
Standard Deviation
Today’s Objective:
I can find and use standard deviation.
Standard
Deviation
Distance from mean
Data
x
182
186
182
184
185
184
185
Deviation
𝑥−𝑥
−2
2
−2
0
1
0
1
Mean: 𝑥 = 184
(Deviation)2
(𝑥 − 𝑥)2
4
4
4
0
1
0
1
Variance:
average of squared deviation
2
(𝑥
−
𝑥)
𝜎2 =
𝑛
𝜎2 = 2
Standard Deviation:
Square root of variance
𝜎=
(𝑥 − 𝑥)2
𝑛
= 1.41
Standard Deviation
Variance:
Data
x
52
63
65
77
80
82
Deviation
𝑥−𝑥
−17.83
−6.83
−4.83
7.17
10.17
12.17
(Deviation)2
(𝑥 − 𝑥)2
317.91
46.65
23.33
51.41
103.43
148.11
2
690.83
(𝑥
−
𝑥)
2
=
𝜎 =
= 115.14
6
𝑛
Standard Deviation:
𝜎=
(𝑥 − 𝑥)2
= 115.14 = 10.73
𝑛
Mean: 𝑥 = 69.83
Round all answers to the nearest hundredth
Using standard deviation to describe data
Pg. 722 #6-14 evens,
16, 17, 18, 21
Year
#
Number of hurricanes in Atlantic Ocean from 1992 to 2006
1
2
3
4
5
6
7
8
9 10 11 12 13
4
4
3 11 10 3 10 8
8
9
4
7
9
1. Find the mean, variance and standard
deviation for the number of hurricanes.
2. Within how many standard deviations of
the mean do all the values fall?
• Create a dot plot of the hurricanes.
mean
3.21
3.21
3.21
3.21
mean:
Variation:
14
14
15
5
7.27
10.30
standard deviation 3.21
Data falls with 3 standard
deviations of the mean
3.21
3.21