Question

**Explain how the scattering of raw scores throughout a
distribution would**

**affect the standard deviation. That is, how would the
standard deviation be affected if**

**the data points were very tightly clustered versus if
they were quite spread out?**

Answer #1

Standard deviation measures the spread of data values in a distribution. It is measured using the deviation of each data value from the mean. The standard deviation increases, if data values have higher deviation, which means, the more scattered data values are, the higher standard deviation it will have.

If the data points were very tightly clustered, the standard deviation will be very low. If all points are the same, that is there is no deviation from the mean, the standard deviation is 0.

A normal distribution of scores has a standard deviation of 10.
Find the z-scores corresponding to each of the following
values:
A score that is 20 points above the mean.
A score that is 10 points below the mean.
A score that is 15 points above the mean
A score that is 30 points below the mean.

1. It is useful to know how spread out the scores are. Which one
of the following is not a measure of "spread" among the scores?
variance
standard deviation
mean
range
2. Which descriptive statistic would depend directly on the
sample size (number of data points) in the calculation process?
Standard deviation
Median
Range
Mode
3. To gather feedback on a new iPhone app, users are asked to
rate the app on a scale of 1 to 5 in terms...

, how does a large or small standard deviation affect the shape
of the Normal Distribution curve?

A distribution of scores on a math exam has a mean of 88 and a
standard deviation of 12. The instructor would like to curve the
exam by adding 2 points to all exams. What will the new mean,
variance, and standard deviation be (show your work – you may type,
hand write, or take a picture of a hand-written solution)?
What is the new mean, variance, and standard deviation?

Calculate the sample standard deviation and sample variance for
the following frequency distribution of scores in a statistics
class. If necessary, round to one more decimal place than the
largest number of decimal places given in the data.
Scores
Class
Frequency
56 - 64
13
65 - 73
9
74 - 82
4
83 - 91
10
92 - 100
6

1. "The mean of a sample of 10 scores is 100, and the standard
deviation is 5. For the following raw scores, compute the z
score:
101
112
97 .
For the following z scores, work backward to compute the
corresponding raw score:
0.5
1.1
2.12
2. "If a student receives a z score of 0, how well did that
student do in comparison with other students in the group?"
3. "You are in charge of a project that is...

Explain fully how the average, standard deviation, and
distribution of means of samples changes as the sample size
increases.

Given the mean of the difference scores is 7.0,
standard deviation of the difference scores is 2.8, and there were
25 in the sample, solve for the following problems, showing all
work to receive full credit:
6) Solve for the standard
error of the difference scores:
Work:
Answer:
7) Calculate the
correlated-groups t test to determine the
tobt.
Work:
Answer:
8) If this is a
non-directional test, what is the t
cv?
(No work needed)
Answer:
Identify the statistical test...

How are variance and standard deviation related? If
s=0 what must be true about the scores in the distribution? Verify
your answer using an example.

1. Let the mean be 100 and the standard deviation be 15 for the
normal distribution for adult IQs in North Carolina.
a. Use the empirical rule to find what proportion of the data is
located between 85 and 115.
b. How about 100 and 130?
c. Find the z-score for the following data points and explain
what these mean: i. x = 80 ii. x = 109

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