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The empirical rule states that for normal distribution nearly all data will fall into one of
three deviations of the mean. I took on the topic of boys and their voices getting lower
and or deeper for an example. Boys ages where their voices get deeper have to get
distributed normally so it fits in the category. The average age for a boys voice to lower
and or get deeper is thirteen with deviation of one point two years. This follows the
empirical rule because were on topic of normal age the boys get their depend and or
lowered voices when they reach around thirteen years of age. There are some who get it
before thirteen years of age and some who get it after the age of thirteen. First deviation,
sixty eight percent and is the ages eleven point eight to fourteen point two. Second
deviation, is ninety five percent and is the ages ten point six to fifteen point four. The
third and final deviation is ninety nine percent and is between the ages nine point four
and sixteen point six. My research into the NBA player heights revealed a mean height
of 79 inches with a standard deviation of 3.5 inches, forming a roughly normal bell-
shaped curve. The tallest player had a height of 91 inches. Using the 68-95-99.7 rule as
applied to this situation means that 68% of players fell within one standard deviation of
the mean. Specifically, 68% of players had heights between 75.5 and 82.5 inches.
Likewise, the second standard deviation included 95% of players that had heights
between 72 inches and 86 inches. The third standard deviation represented 99.7% of
players that had heights between 68.5 inches and 89.5 inches. I believe this data to be
true because the the tallest player is so close to the third standard deviation. He would
represent the tallest 0.15%. As we know, there must be a tallest player and a shortest
player. Combined, they account for 0.30% of the population. Based on the sample size,
0.30% equates to 2 people: one is the tallest player and one is the shortest player. In this
respect, the distribution curve appears to reflect accurately. The empirical rule can be
used to find the normal distribution of the heights of women to follow a bell-shaped
distribution with a mean of 160cm, and a standard deviation of 7.5cm.
In this example we are trying to find out what the approximate percentage of women
between 137.5cm and 182.5cm are.
To find the empirical rule in this example, first you find the number of standard
deviations by finding the mean of 160 and multiply it by 7.5, which equals 182.5, then
you add to k by subtracting 160 by both sides, lastly you divide both sides by 3, and
there are 3 standard deviations. Using the empirical rule, the approximate percentage of
the woman's height between 137.5cm and 182.5cm averages 99.7%
The margin of error considers the z score associated with the confidence interval and the
standard error. The standard error indicates the standard deviation in the population of all
possible means (or proportions) drawn from the population.
Also known as three sigma rule or 68-95-99-7 rule. Statistical rule states that a normal
distribution observes data which almost falls within the three standard deviation of the
mean, or average.
In particular, the empirical rule predicts that 68% of observations falls within the first
standard deviation ± σ), 95% within the first two standard deviations ± 2σ), and
99.7% within the first three standard deviations ± 3σ).
Empirical research can be conducted and analyzed using qualitative or quantitative
methods.
Quantitative research: Quantitative research methods are used to gather
information through numerical data. It is used to quantify opinions, behaviors or
other defined variables. These are predetermined and are in a more structured
format. Some of the commonly used methods are survey, longitudinal studies,
polls, etc.
Qualitative research: Qualitative research methods are used to gather non
numerical data. It is used to find meanings, opinions, or the underlying reasons
from its subjects. These methods are unstructured or semi structured. The sample
size for such a research is usually small and it is a conversational type of method
to provide more insight or in-depth information about the problem Some of the
most popular forms of methods are focus groups, experiments, interviews, etc.
Data collected from these will need to be analyzed. Empirical evidence can also be
analyzed either quantitatively and qualitatively. Using this, the researcher can answer
empirical questions which have to be clearly defined and answerable with the findings
he has got. The type of research design used will vary depending on the field in which
it is going to be used. Many of them might choose to do a collective research involving
quantitative and qualitative method to better answer questions which cannot be studied in
a laboratory setting.
Let’s say the population size of wild animals in a zoo is said to be normally distributed.
On an average, one animal has a lifespan of 13.1 years, and the standard deviation is 1.5
years. For determining the probability of a wild animal living more than 14.6 years, one
can consider using the empirical rule. As mentioned earlier, the average of distribution
being 13.1 years, there will be following age ranges determined for every standard
deviation.” (Gordon, 2021).
The empirical rule is used to predict the final results in statistics. This means that an
estimation will exist between the two standard deviations of the mean. The empirical rule
would be used in this scenario to figure out the probability of an animal in the zoo of
living at least 14.6 years. This example gives clear numbers to base the probability
theory off of. Following the trends and patterns of the animals life spans within the zoo
could make a great comparison to each other in order to find out a number. Not every
example is easy.
An example of how the Empirical Rule works within my organization, I leveraged both
Investopedia.com and Images found on Google to ensure my understanding was mostly
on point; showing myself grace if not, as this is new for most if not all of us. My
takeaway is that a call center can take data based on historical data to assess how many
team members take a percentage of calls each day. From this analysis it can be
determined that X number of calls are managed by a single person each day, and a
standard deviation can be considered. An analyst is then able to leverage the Empirical
Rule to further breakdown the analysis and identifying the best approach for the
company. A situation in which the empirical rule can be applied would be measuring
heights of people. You can choose a sample set of people and get all of their heights in
inches and gather all the data. Typically, you will have some shorter, majority average
height and then some taller which would follow a normal distribution. However, when
graphed, you can see that more than likely, it will be a bell shaped curve with majority
of people falling into an average height category. This follows the empirical rule because
each set will fall into a different deviation whether one, two or three standard deviations.
With this example you would need to select a diverse population and not all from
specific areas who would have identical/similar heights. Analysts use the empirical rule
to predict the probabilities and distributions of the outcomes they are studying. This rule
also helps determine what outliers are within the data captured. The mean and the
standard deviation are valuable pieces of data since it allows to calculate the probabilities
and percentages for various outcomes. Upon my research to determine ways the
Empirical Rule I discovered a site that showed the graph for Distribution of Pizza
Delivery Times. Per the page Statistics by Jim "A pizza restaurant has a mean delivery
time of 30 minutes and a standard deviation of 5 minutes" This information provides the
employer with how long it is taking the customers to receive their pizza. It also can help
the employer determine which of their employees are delivering pizzas in a timely matter
and which ones are not being as productive. In statistics, the empirical rule is used for
the purpose of forecasting the final outcome. After the calculation of the standard
deviation and prior to collecting the exact data, the empirical rule can be used to arrive
at a rough estimate of the outcome of the impending data for collection and analysis.
The use of the probability distribution is considered important as it can be used as
interim heuristic (Artyushenko et al., 2020). A situation in which the data that is
collected for representing the situation follows a normal distribution involves three
students playing basketball, out of which one of them is a good player, one of them is
an average player, and the third one does not know how to play the sport (Artyushenko
et al., 2020). In the specific situation, the good player is likely to make the most score,
whereas the average player is likely to make a few shots while playing the game. On the
other hand, the student who does not know how to play basketball may not be able to
play it at all. The situation follows empirical rue since there is a normal distribution of
the game scores. The key benefit that may exist because the situation has data that is
distributed normally is that probability can be ascertained from the information. During
the recent election season, you saw many instances where polls were taken and reported,
along with the confidence level of the estimate. For example, a poll showed that one
candidate had a ""voting for" level of 37%+/-4. The opposing candidate had a score of
39%+/-4 at a 95% confidence level. Because the poll is not a census sample, a sample
may be "good" but will have variation around the TRUE population proportion or mean.
Thus, the poll is an estimate. The +/- value establishes a range within which the true
population proportion is said to be, given a certain level of confidence. The empirical
rule is when pieces of data will fall within 3 standard deviations of the mean in a normal
data set. It is also referred to the 3 sigma rule “68-95-99.7 rule”. The reason for this is
the first standard deviation from the mean, 68% of data rests, 95% of data will fall
within the 2 standard deviation, and nearly 99.7% of all data falls within the 3 standard
deviations. This rule can be useful for forecasting final outcomes within a data set.
A situation where you can collect data and the empirical rule applies is finding the
probability that an average animal at the zoo will live longer than 14.6 years. The
distribution means is 13.1 years old and standard deviation lifespan is 1.5 years.
Thefirst standard deviation 13.1-1.5 to 13.1 + 1.5 or 11.6 to 14.6.
Twostandard deviation 13.1- (2 x 1.5) to 13.1 + (2 x 1.5), or 10.1 to 16.1
Threestandard deviations 13.1 - (3 x 1.5) to 13.1 + (3 x 1.5), or, 8.6 to 17.6
The probability of the animal living for more than 14.6 years is 16% because the
remaining 32% of the distribution is outside the range. One half is above the range of
14.6 and the other below 11.6.
In statistics, the empirical rule states that 99.7% of data occurs within three standard
deviations of the mean within a normal distribution. To this end, 68% of the observed
data will occur within the first standard deviation, 95% will take place in the second
deviation, and 97.5% within the third standard deviation. The empirical rule predicts the
probability distribution for a set of outcomes. d
The empirical rule is applied to anticipate probable outcomes in a normal distribution.
For instance, a statistician would use this to estimate the percentage of cases that fall in
each standard deviation. Consider that the standard deviation is 3.1 and the mean equals
10. In this case, the first standard deviation would range between (10+3.2)= 13.2 and (10-
3.2)= 6.8. The second deviation would fall between 10 + (2 X 3.2)= 16.4 and 10 - (2 X
3.2)= 3.6, and so forth. Now, on a personal note, this looks like my retirement plan.
Seriously, when I go on my retirement plans (401k and define benefit), those formulas
look exactly like, how I am supposed to retire. I put in a certain percentage in my 401k,
my employer matches, and then with the define benefit (pension employer contribution)
it is on top meaning with minimal loss. My 401K, fluctuate with distributions and the
stock market plays a key role into it as well.My retirement can go up, rest, and fall (bell
curve). The way I am paid is by a percentage, and if I work more one week than the
other, my distributions differ. Next, if the stock market and my bonds go up, my
retirement goes up, then, it can just rest. Meaning, if no change is in the market so
everything sits at the top of the bell. The real tick off, and I do apologize class for the
term, for as my personal life, inflation, the price of food, gasoline, energy, natural gas,
and my stress level from all of this.
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