Question

What is the meaning of variance and standard deviation? (I understand how to calculate them, but understanding the concept behind them is confusing.)

What happens if the variance calculated is the same as them mean? What is the meaning behind these numbers? For example, you roll a 6 sided dice and each possibility is equally likely. Then both the mean and variance is 3.5.

Answer #1

Variance is a measure of variability/spread of data. For example, let's say we have two data sets:

1,4,8,10,7 and 6,6,6,6,6

I have deliberately chosen these two examples. As you may observe, both these have 5 observations with mean = 6. But the first data varies from 1 to 10 while the second one remains constant at 6. The first data varies considerably around its mean 6 while the second one doesn't vary at all. Thus we can say that the first data has got some variance while the second has none.

The standard deviation is the square root of the variance. Since the variance contains the mean of squared errors, we can't use it directly to compare with our raw data. For ex. assume that the above data is the marks of 5 students out of 10. The variance will have a unit of (marks^2). When we take its square root, then only we can compare (see how far a certain score lies from the mean, normalised according to the standard deviation).

Generally, variance being equal to the mean doesn't have any mathematical significance. Both should be interpreted individually.

I am trying to figure out the probability, expected value,
variance, and standard deviation for a series of dice rolls. For
example, if I roll a six-sided die in an attempt to roll a 1, and
it takes me 13 rolls before a 1 appears, what are those answers? I
believe I have figured out the probability equation:
P(P-1)^x where x is the number of rolls - 1 so for 13 rolls the
probability would be: 1/6(1-1/6)^12 = .01864045
Is...

Assignment III
1) Use the non-machine formula to calculate the variance and
standard deviation from the following data
Herd 1
67 62 69
72 68 68
71 69 65
71 70 64
64 66 71
67 75
2) What is the probability that one card selected from a deck of
52 is a club or a number card or both?
3) A container contains 10 green tennis balls and 7 orange
tennis balls. What is the probability of drawing 2...

I am having trouble deciding what is true for these questions. I
thought I had the right answers but they keep getting marked wrong.
For Question 1, I chose option 2, as I though all the others to be
false. For Question 4 I chose option 4, as I learned that the
z-scores of the mean and standard deviation were always 0 and 1,
respectively. For question 5 I chose option 4 as well.
Which one of the following statements...

1. Indicate if each of the following is true or false. If false,
provide a counterexample.
(a) The mean of a sample is always the same as the median of
it.
(b) The mean of a population is the same as that of a
sample.
(c) If a value appears more than half in a sample, then the mode
is equal to the value.
2. (Union and intersection of sets) Let Ω = {1,2,...,6}. Suppose
each element is equally likely,...

Texas is home to more than one million undocumented immigrants,
and most of them are stuck in low-paying jobs. Meanwhile, the state
also suffers from a lack of skilled workers. The Texas Workforce
Commission estimates that 133,000 jobs are currently unfilled, many
because employers cannot find qualified applicants (The Boston
Globe, September 29, 2011). Texas was the first state to pass a law
that allows children of undocumented immigrants to pay in-state
college tuition rates if they have lived in...

If you run summary() command on a result of linear model fitting
returned by lm(), you will see a column Pr(>t). You could guess
that it is a result of some t-test. How does it apply here? So far
we have seen t-tests in the settings of testing sample locations.
The ingredients were: 1) null hypothesis: in earlier cases we
looked into the null that stated that two samples came from the
distribution(s) with the same mean(s); 2) test statistic:...

Task 1: Read each of the scenarios. Explain how one or
both fit into one of the three theories illustrated by the
experiments. Be specific using at least two (2) psychological terms
(underline/boldface them), the psychologist and his experiment
(underline/boldface them), and the evidence that supports or
refutes what the experiment theorized. Be sure to illustrate the
scenario and the specific parts of the scenarios as they fit into
your explanation so I can see your full understanding.
Task 2:...

BridgeRock is a major manufacturer of tires in the U.S.. The
company had five manufacturing facilities where tires were made and
another 20 facilities for various components and materials used in
tires. Each manufacturing facility produced 10,000 tires every
hour. Quality had always been emphasized at BridgeRock, but lately
quality was a bigger issue because of recent fatal accidents
involving tires made by other manufacturers due to tread
separation. All tire manufacturers were under pressure to ensure
problems did not...

What Happens When Hospitals Run out of Ventilators and Other
Emergency Rescue Equipment?
Patricia Benner, R.N., Ph.D., FAAN
April 7, 2020
Our overwhelmed, or soon to be overwhelmed hospitals, face
rationing precious life-saving equipment, such as ventilators. Our
national lack of preparedness for a global pandemic will, in the
near future, force local physicians and nurses to ration
ventilators and oxygen delivery equipment, for patients and
Personal Protective Equipment (PPE) for caregivers. How do health
care providers make decisions about...

I am unsure of what is unclear. The instructions are:
1. Set up a worksheet for the solvency ratios--current
ratio and the quick ratio.
2. Compute these ratios for Doctors Smith and Brown. To
do so, you will need one additional piece of information that is
not present on the doctors’
statements: their maximum annual debt service is
$22,200.
Practice Exercise 11–II: Solvency Ratios
Refer to Doctors Smith and Brown’s financial statements
presented in the preceding Chapter 10.
Required
1....

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 29 minutes ago

asked 46 minutes ago

asked 49 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago