Question

What is the difference between data that is normally distributed versus data that is not? What can you say about small sample sizes? How many standard deviations from the mean is considered unusual and why?

Typed responses only please :)

Answer #1

For a normally distributed data, the graph is symmetric about the mean, in such cases mean , Median and mode are equal . It has a bell shaped curve structure. Where as the data is not normal may have many modes , and the graph may be skewed, non symmetric and so on.

According to the central limit theorem, if the sample size is sufficiently large enough then the sampling distribution of the sample mean is approximately normal regardless of the distribution of the sample.

*Data beyond two standard deviations away from the mean is considered "unusual" data.As a general rule, z-scores lower than -1.96 or higher than 1.96 ( 2 tailed)

arec considered unusual and interesting. That is, they are statistically significant outliers.

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If you take a sample of size 13, can you say what the shape of
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If the sample size is 13, then you can't say anything about the
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You are sampling from a normally distributed set of data with μ
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samples?c) One sample had a mean of 151. Is this unusual? Why or
why not?

You are sampling from a normally distributed set of data with μ
= 155 and σ = 16. You have taken samples of this data with sample
size of 64 data elements. a) What is the expected mean of your
samples?b) What is the expected standard deviation of your
samples?c) One sample had a mean of 151. Is this unusual? Why or
why not?

1. Given that the heights of 300 students are normally
distributed with a mean of 68.0 inches and a Standard Deviation of
3.0 inches, determine how many students have heights...
(a) ... greater than 71 inches
(b) ... less than or equal to 65 inches
(c) ... between 65 inches and 71 inches inclusive
(d) ... between 59 inches and 62 inches inclusive
Assume the measurements are recorded to the nearest inch.
2. If the mean and standard deviation of...

1. Men’s heights are normally distributed with a mean of 69" and
a standard deviation of 2.5". Draw the distribution curve; label
the mean and 3 standard deviations above and below the mean. Answer
the following question:
a. Between what heights do 68% of men fall?
b. What percentage of men are shorter than 74"?
c. What percentage of men are taller than 65"?
2. The middle 95% of adults have an IQ between 60 and 140.
Assume that IQ...

Male Heights: Assume heights and weights are
normally distributed variables with means and standard deviations
given in the table below.
Strata
Mean
Standard Deviation
Mean
Standard Deviation
Height
Height
Weight
Weight
(inches)
(inches)
(pounds)
(pounds)
U.S. Men
69.1
2.9
191
28
U.S. Women
64.0
2.8
145
32
NFL Quarterbacks
76.5
1.8
245
25
Top Female Models
70.0
2.2
115
18
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1.With any set of scores that is normally distributed, what
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a.between the mean and a score that lies one standard deviation
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b. between the mean and a score that lies one standard deviation
below the mean?
c. between the mean and a score that lies two standard
deviations below the mean?
d. between a score that lies three standard deviations below the
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