Normal distributions are very informative in statistics, it is type of continuous distribution. It is often used in both natural and social sciences to help shed light on random variables where their distri-bution is not known.
The three features of normal distribution are
1. It has a bell shaped curve.
2. The total areas under the curve is equal to 1.
3. The bell shape is symmetrical.
2. How is the average of a normal distribution measured and what should be the relationship be-tween the three types of measurement?
There are three types of measure in order to support the average of normal distribution.
They are: The mean summarizes the properties of the group. It’s important to understand that the mean does not represent an individual – there may be no individual whose value matches the mean; but the mean is a summary of the entire population. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. The sum divided by the count.
The median is almost always more representative of a typical member of a group. If you take all of the numbers in a list, and arrange them from lowest to highest, or vice versa, if there is an odd number, the number at the middle will be the median. If there is an even number, the median will be the average of the middle two numbers. Unlike the mean, the
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It establishes how far they have deviated from the mean in either direction. It gives us detail about the proportion of the distribution are -1 and +1 from the standard deviation, as well two standard deviations from the mean. This can be useful in measuring differences within a group of participants. For example, in a class where the mean is 50% for both boys and girls, looking at the standard deviation can show how much each gender deviated from the mean and can highlight the spread of scores. This can be a more useful
I have four quiz scores: 94, 93, 85, and 0. what is the mean (average) of my quiz scores? Would you code this as a factor or a numeric value in R?
Answer: Outliers are necessary to be detected in the scatter plot because they are abnormal values and they can cause skewness in the data plots. They can also impact the results.
After reading this book, I am touched by the underlying philosophy of statistics. Various theories and models are introduced in this book. During the progress of the development, controversies and confits among these theories are largely attributable to diversity of ideology and doctrine from their establishers. In future, the statistics might evolve into a new era and the vogue methods, like p-value or confidence interval, might be discarded. I am looking forward to witness how statistics make our lives
This process is done by administering the test to a representative sample and using these scores to establish standards, usually referred to as norms, by which all individual scores can be compared. Since the average score is 100, experts can quickly evaluate individual test scores against the average of others to determine where these scores fall on the normal distribution.
A continuous random variable X is said to follows a normal distribution with parameter μ and σ (or μ and σ2) if the probability functions is
The median wage is the wage at which half the workers in an occupation earned more than that amount and half earned less. The lowest 10 percent earned less than $20,580, and the top 10 percent earned more than $42,400.
At the Group level, individuals share similar characteristics with their counterparts in the same group. Different groups are identified by race, gender, class among others. Individuals within a collective group share similar beliefs, values, social practices, and rules.
The standards create a form of consistency for each student, which gives equal opportunity for each student across the United States. A benefit to the standards remaining the same across states is a student can move around America and still expect the same curriculum. Also teachers, parents, and students know what is expected in school due to the standards. Parents are able to keep up with what their child is doing since the parent knows what is expected among every grade. The standards focus on getting a student prepared for college.
Possible sources of error in this experiment include the inaccuracy of measurements, as correct measurements are vital for the experiment.
In evaluating statistical data one thing to consider is the measure that is used. By understanding the different statistical measurement tools and how they differ from one another, it is possible to judge whether a statistical graph can be accepted at face value. A good example is using the mean to depict averages. This was demonstrated by using the mean as a measure of determining the distribution of incomes. The mean income depicted was, $70,000 per year. At face value, it looks as though the sample population enjoys a rather high income. However, upon seeing individual salaries, it becomes obvious that only a few salaries are responsible for the high average income as depicted by the mean. The majority of the salaries were well under the $70,000 average. Therefore, the mean distributed income of $70,000 was at best misleading. By also looking at the median and mode measures of the income distributions, one has a clearer picture of the actual income distributions. Because this data contained extreme values, a standard deviation curve would have given better representation of salary distribution and would have highlighted the salaries at the high level and how they skewed the mean value.
__C__ 8. Which of the following scales would be used when the information is qualitative rather than quantitative?
Probability and Statistics most widespread use is in the arena of gambling. Gambling is big all over the world and lots of money is won and lost with their aid. In horse racing especially the statistics of a horse in terms of its physical condition and winning history sway numbers of persons into believing that the mathematical evidence that is derived can actually be a good indicator of a race’s outcome. Usually it is if the odds or probability are great in favor of the desired outcome. However the future is uncertain and races can turn out any of a number of different ways.
General uncertainty – the quality of the readings of most instruments decreases over time due to any number of environmental and internal factors, as frequent calibration is necessary. When several consecutive incorrect readings are taken for a liquid of known specific density, it is clear that the hydrometer is out of
The Gaussian distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. It is a very commonly occurring continuous probability distribution. In theory, Gaussian distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known. Gaussian distributions are also sometimes referred as Bell curve or normal distribution.
c. Statistical Design: It concerns with the question of how many items are to be observed and how the information and data gathered are being