What Is Statistics In Math

Career Differences For Math Vs Statistics Major

While mathematicians and statisticians do a similar job. They apply mathematical and statistical approaches to data analysis. There are notable differences in their professional paths. For beginners, a statistician is a more extensive occupation in the United States than a mathematician. With 37,200 statistician employment vs 3,100 mathematician jobs.

Both fields are quickly developing. But statisticians are expected to grow faster and have a far bigger rise in overall job opportunities than mathematicians.

Mathematicians will likely have a 30 percent job growth over the next decade, resulting in 900 new employment chances. In contrast, statisticians will notice a 34 percent job growth rate, resulting in 12,600 new job chances.

Although there are fewer mathematicians than statisticians. Mathematicians make more money. Statisticians earn an average of $84,060 over all industries, compared to the median pay of $103,010 for mathematicians. It is the career comparison between Math vs Statistics.

Mathematicians earn a median annual income of $120,840 in the highest-paying industries for these occupations, compared to $103,630 for statisticians.

Now, what do you think!

What Is The Difference Between Mathematics And Statistics

Students often find Statistics as a subset of Maths, merged within the other topics. While some mathematicians kindly disagree with that idea, others despise it. The latter, pure mathematicians, find it too imprecise to be called maths. The former consider it an extension of Maths. The two subjects complement each other and function on similar methodologies. A strong grasp of maths can facilitate a better understanding of statistical techniques. Both subjects are introduced to children in school. However, statistics isnt as prominent in the curriculum at most places. Maths is taught extensively and with much more fervour. Students who major in these subjects gain invaluable knowledge and lucrative career opportunities. Beyond academics, both subjects enhance the childs cognitive and soft skills.

What Kind Of Math Is Statistics

This can be answered as to how you can apply statistics in math. Statistics considered as a part of applied mathematics that uses probability theory.

The theory can use to simplify the collected sample data. It supports characteristics of probability where the data generalizations are TRUE. You can refer to it as statistical inference.

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Statistical Levels Of Measurement

After analyzing variables and outcomes as part of statistics, there are several resulting levels of measurement. Statistics can quantify outcomes in these different ways:

What Do Exactly The Statistics Include

It includes the measure of dispersion and the measure of central tendency.

Here, the dispersions consist of standard deviation and variance, whereas the measure of central tendency consists of mean, median, and mode.

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Data Representation In Statistics

The collection of observations and facts is known a data. These observations and facts can be in the form of numbers, measurements, or statements. There are two different kinds of data i.e. Qualitative data and quantitative data. Qualitative data is when the data is descriptive or categorical and quantitative data is when the data is numerical information. Once we know the data collection methods, we aim at representing the collected data in different forms of graphs such as a bar graph, line graph, pie chart, stem and leaf plots, scatter plot, and so on. Before the analysis of data, the outliers are removed that are due to the invariability in the measurements of data. Let us look at different kinds of data representation in statistics.

What Exactly Is Statistics

Statistics is a department of applied mathematics. It collects, defines, analyzes, and judges conclusions from numerical data. Differential and integral calculus, linear algebra, and probability theory are used in statistics mathematical ideas.

There are two types of Statistics. Descriptive statistics, which explains the features of sample and population data. And inferential statistics, which uses those properties to test data and make conclusions.

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Information Technology/computer Science And Programming:

Mathematics and statistics have long been an integral component of IT and computer science, and these are areas that mathematicians and statisticians have traditional found employment in. Career opportunities in this sector have been broadening, particularly as concerns about cybersecurity have intensified. Professional cybersecurity and IT resources include:

• Information Systems Security Association

Definitions Of Statistics Probability And Key Terms

The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.

COLLABORATIVE EXERCISE

In your classroom, try this exercise. Have class members write down the average time they sleep per night. Your instructor will record the data. Then create a simple graph of the data. A dot plot consists of a number line and dots positioned above the number line. For example, consider the following data:

5 5.5 6 6 6 6.5 6.5 6.5 6.5 7 7 8 8 9

The dot plot for this data would be as follows:

Figure \

Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not?

Where do your data appear to cluster? How might you interpret the clustering?

The questions above ask you to analyze and interpret your data. With this example, you have begun your study of statistics.

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Mathematics And Statistics: Popular Courses

Now that we have explored the key factors for the question on what is the difference between Mathematics and Statistics, lets have a look at the courses offered under both disciplines. Although, it must be noted that there are quite a few courses, especially at the postgraduate level which are interdisciplinary in nature, essentially borrowing from both the fields of study. Here are some of the popular courses offered under Mathematics and Statistics:

What Is An Algorithm

In the simplest terms, an algorithm is a set of step-by-step instructions for completing a particular task or a discrete series of operations. When used in conjunction with quantitative data and statistical probability modeling, an algorithm becomes a powerful tool for complex analyses, decision-making, automated reasoning, and machine learning. Much of what we think of as computer programming is, in fact, algorithmic in nature. A common type of algorithmic coding involves an if/then instruction, such as, if the numerical value is greater than ten, then subtract three if the numerical value is less than five, then add three.

To explore algorithms further, consult the following resources:

Harvard University computer scientist David J. Malan narrates a TED-Ed animated video on Whats an Algorithm?

Software developer and former University of Iowa mathematics professor Alexander Bogomolny maintains Interactive Mathematics Miscellany and Puzzles, a website dedicated to mathematics that has a section on What is Algorithm?

The BBC has a multi-media webpage that offers an overview of several approaches to understanding What is an Algorithm?

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Residual Equation In Math

Given the linear regression model which includes the residual for estimation, you can write:

where \ is the response variable , \ is the intercept, \ is the slope of the line, \ is

the explanatory variable and \ is the residual.

Hence, the predicted value of \ will be:

Then using the definition, the residual equation for the linear regression model is

where \ represents residual, \ is the actual value and \ is the predicted value of y.

For \ observations of data, you can represent predicted values as,

And with these \ predicted quantities residuals can be written as,

This equation for residuals will be helpful in finding residuals from any given data. Note that, the order of subtraction is important when finding residuals. It is always the predicted value taken from the actual value. That is

residual = actual value predicted value.

Examples For Small Values

First we will look at a few examples of the factorial with small values of n:

• 3! = 3 x 2 x 1 = 6
• 4! = 4 x 3 x 2 x 1 = 24
• 5! = 5 x 4 x 3 x 2 x 1 = 120
• 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
• 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
• 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
• 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362880
• 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

As we can see the factorial gets very large very quickly. Something that may seem small, such as 20! actually has 19 digits.

Factorials are easy to compute, but they can be somewhat tedious to calculate. Fortunately, many calculators have a factorial key . This function of the calculator will automate the multiplications.

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Testimonials From Recent Students

Hoxie AckermanLooking back on my time in the Boston University Mathematics & Statistics department, I was constantly impressed by the high caliber of professors and the breadth of courses offered. The skills I acquired through my coursework and class projects made me an attractive job candidate to a variety of organizations and helped me secure a great position at a local biotech company weeks after graduation. Furthermore, the BA/MA program is an incredible opportunity the additional coursework and degree have both enhanced my ability to succeed at my job and prepared me for top PhD programs. Strong mathematicians and statisticians will play a prominent role in almost every field in the twenty-first century, and a degree from the Boston University Mathematics & Statistics department will serve you well for many years to come.

Mathilde Kaper : I was unsure of what I wanted to major in, but this quickly changed once I started taking more math and stat classes at BU. Couldnt have asked for a better group of professors who clearly are there due to their love of their subjects and desire to inspire others. They made time to make sure that you understood the material and they were there to see to it that you succeeded. One word of advice: make sure to ask lots of questions! And remember that there are so many companies out there that need Statisticians. Because of my BA/MA in math/stats, I have found a job which I really love.

A Comprehensive Guide On What Is Statistics In Math

Statistics and math are two different things for data scientists. Really? But I thought statistics is the branch of mathematics!!

I think the author has written it wrong 😀This is what you might be thinking after reading the first statement.

But let me clear to you that statistics and math are not the same things. How do they differ? Well, I have answered it below. But before that, let me explain to you the purpose of this blog.

When it comes to statistics and mathematics, most of the students get frightened. And it is always like:

If you are one of those students and thinking is statistics easier than pure math, you are at the right place.

I have answered almost all kinds of questions that arise in your mind regarding what is statistics in math and provided various important information.

So, without wasting much time, lets start with a new concept of statistics in math.

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What Is Statistics In Maths

In Mathematics, statistics concerns the collection of data, organisation, interpretation, analysis and data presentation. The main purpose of using statistics is to plan the collected data in terms of experimental designs and statistical surveys. Statistics is considered a mathematical science that works with numerical data. In short, statistics is a crucial process which helps to make the decision based on the data.

Masters Degrees In Mathematics And Statistics

A bachelors degree in mathematics and/or statistics can offer sufficient training for entry-level positions in a range of fields, but it is often a way of preparing for further training in a masters degree program. At the graduate level, this training gets more specialized, and includes degrees in areas like: Actuarial Science Applied Mathematics Applied Statistics Biostatistics Computer Science and Information Technology Data Science and Analytics Math Education Mathematical Engineering and Pure Mathematics or Mathematical Theory. These may be Master of Arts or Master of Science degrees, and there are also Master of Education degrees for those aiming to teach math at the primary, secondary, high school, and/or community college level.

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Residual Examples In Math

You can understand how to calculate residuals more clearly by following the residual examples here.

A shop attendant earns \ per month. Assuming the consumption function for this shop attendant is given by \, where \ is consumption and \ is income. Assuming further, that the shop attendant spends \ monthly, determine the residual.

Answer:

First, you have to find the estimated or predicted value of \ using the model \.

Hence, \

Given \, you can compute the residual as:

Therefore, the residual equals \. This means you predicted the shop attendant spends lesser ) than they actually spend ).

Consider another example to find the predicted values and residuals for the given data

A production function for a factory follows the function \. Where \ is the output level and \ is the material used in kilograms. Assuming the firm uses \ of input, find the residual of the production function.

Answer:

The firm uses \ of input, so it will also be the actual value \. You want to find the estimated output level. So

Then you can estimate the residual or error of prediction:

Therefore, the predicted output level is larger than the actual level of \ by \.

The following example will show the plotting of residuals in the graph.

Sam collected data on the time taken to study, and the scores obtained after the given test from the class. Find the residuals for the linear regression model \. Also, plot the residuals in the graph.

Now Lets Understand The Key Comparison Of Statistics Vs Math

It is quite important to know the difference between statistics and math to understand what is statistics in math.

These are essential elements for any data scientist. But some view statistics as a math discipline, but in reality, both are completely different.

Math is related to numbers that have detailed answers, whereas statistics make sense of numbers using guesses.

Still confusing??

Lets see the key differences between statistics and math.

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