ap stats bw 9/17 1)which set has the largest standard deviation? the smallest? a. 0 10 20 30 40 b. 0...
TRANSCRIPT
![Page 1: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/1.jpg)
AP Stats BW 9/171) Which set has the largest standard deviation? The smallest?
a. 0 10 20 30 40b. 0 0 20 40 40c. 0 19 20 21 40
2) Without calculating, which data set has the greatest standard deviation? Which has the smallest?
How are the data sets the same? How do they differ?
![Page 2: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/2.jpg)
Section2.4 – Normal Distributions
SWBAT: Identify and analyze patterns of distributions using shape, center and spread.
Source: www.stat119review.com
![Page 3: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/3.jpg)
Normal DistributionsMany real-life data sets have distributions that are approximately symmetric and bell-shaped. Sometimes, the overall pattern of a large data set can be described by a smooth curve
Many measurements, including heights,
weights, and IQ’s will have a normal curve
when the data set is large.
The distribution whose shape is described by
a normal curve is called a normal
distribution.
![Page 4: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/4.jpg)
Normal Distribution, cont’d
Characteristics of Normal Distributions:
• The mean and the median are the same value.
• Symmetric and bell-shaped.
• The area under the curve is exactly 1 or 100%.
• The spread is completely measured by a single number, the standard deviation.
• Good approximation of chance outcomes
![Page 5: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/5.jpg)
Normal Distribution, cont’d
The standard deviation of a normal curve can be found directly from the curve.
The point where the normal curve changes “curvature” on either side of the curve is the standard deviation.
Same mean - different standard deviations.
![Page 6: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/6.jpg)
Emperical Rule (68 – 95 – 99.7 Rule)
For data with a bell-shaped distribution, the standard deviation has the following characteristics:
•About 68% of the data lie within one standard deviation of the mean.
•About 95% of the data lie within two standard deviations of the mean.
•About 99.7% of the data lie within three standard deviations of the mean.
![Page 7: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/7.jpg)
Emperical Rule (68 – 95 – 99.7 Rule)
50% of the data will fall above the mean / 50% below16% of the data falls more than 1 std deviation
above/below the mean99.85% of the data falls above -3 std deviations.
![Page 8: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/8.jpg)
Emperical Rule EXAMPLE 1The distribution of scores on tests such as the SAT exam is close to normal. SAT scores are adjusted so that the mean score is about μ = 500 and the standard deviation is about σ = 100.
1. What percent of scores fall between 200 and 800?
2. What percent of scores fall above 700?
3. What percentile is a student that scores a 600 on the SAT?
500 600 700 800400300200
1) (2.35+13.5+34+34+13.5+2.35) = 99.7%
2) (2.35+ 0.15) = 2.5%
3) (0.15 + 2.35 + 13.5 + 34 +34) = 84TH percentile
![Page 9: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/9.jpg)
Emperical Rule EXAMPLE 2Battery A: 37, 38, 38, 39, 39, 39, 40, 40, 40, 40, 40, 41, 41, 41, 42, 42, 43
Using calculator, we find x-bar = 40 and s = 1.58
The Emperical Rule says appx 68% of the data should fall within 1 std dev of the mean. So if we look at 39 to 41, we see there are 11 items out of the 17
So estimating 11/17 = 65%
Let’s graph the actual curve:
Mean = 40 ± s: 38.42 – 41.58± 2s: 36.84 – 43.16± 3s: 35.26 – 44.74
40 41.58 43.16 44.7438.4236.8435.26
68% of data lies between 38.42 and 41.58 which is pretty close to the estimated 39 – 41.
![Page 10: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/10.jpg)
Emperical Rule EXAMPLE 2, cont’dWe can also take a look at the frequency histogram for Battery A and see that it has a normal distribution. Battery B is also shown. What can you conclude about Battery B?
Both batteries have a mean (and median) of 40, however Battery B has a greater standard deviation than Battery A.
![Page 11: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/11.jpg)
You try….IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
1) What is the percentile for someone with an IQ of 130?
![Page 12: AP Stats BW 9/17 1)Which set has the largest standard deviation? The smallest? a. 0 10 20 30 40 b. 0 0 20 40 40 c. 0 19 20 21 40 2)Without calculating,](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d745503460f94a53e7a/html5/thumbnails/12.jpg)
HOMEWORK:Normal Curve Worksheet and Catch UP