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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. f
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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