the empirical rule standard deviation and the normally distributed data set
TRANSCRIPT
![Page 1: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/1.jpg)
The Empirical Rule
Standard Deviation and the Normally Distributed Data Set
![Page 2: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/2.jpg)
2
Normal Distribution
S -3 -2 -1 0 1 2 3
xData values 2 4 6 8 10 12 14
Data Values567891011
![Page 3: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/3.jpg)
The Empirical Rule
• When– The standard deviation is known– The mean is known– & the data is normally distributed
(like a bell-shaped mound)
• Then– The Empirical Rule can be used to generalize some
properties about the distribution (data)– Also known as the sigma rule; 68-95-99.7 rule
![Page 4: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/4.jpg)
4
Normal Distribution
2.14% 2.14%
S -3 -2 -1 0 1 2 3
0.13% 0.13%
13.59%
34.13%34.13%
13.59%
x
Percent of values under portions of the normal curve
![Page 5: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/5.jpg)
The Empirical Rule• When data is normally distributed:– Approx. 68% of the values will fall within +/- 1 S from
the x
S -3 -2 -1 0 1 2 3
68%
![Page 6: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/6.jpg)
The Empirical Rule• When data is normally distributed:– Approx. 95% of the values will fall within +/- 2 S from
the x
S -3 -2 -1 0 1 2 3
95%
![Page 7: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/7.jpg)
The Empirical Rule• When data is normally distributed:– Approx. 99% of the values will fall within +/- 3 S from
the x
S -3 -2 -1 0 1 2 3
99.7%
![Page 8: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/8.jpg)
Approximate Empirical Calculations
• Approximate Calculations– 68% = x +/- 1(s)• [ x – 1(s), x + 1(s)]
– 95% = x +/- 2(S)• [ x – 2(s), x + 2(s)]
– 99% = x +/- 3(S)• [ x – 3(s), x + 3(s)]
![Page 9: The Empirical Rule Standard Deviation and the Normally Distributed Data Set](https://reader036.vdocument.in/reader036/viewer/2022062423/56649f3a5503460f94c580d6/html5/thumbnails/9.jpg)
SAT Distribution
m = 490 and s = 100