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A Detailed Study Regarding Different Important Areas of Statistics

by May 10, 2019Statistics0 comments

Statistics usually uses mathematical analysis included in models and representations for a particular set of data.

There are different studies included in the data which can be used for gathering and then analyzing the data.

Further conclusions are drawn from such analysis. There are certain measures associated with statistics which are popularly used for analysis and include, mean, variance etc.

Understanding this subject

Statistics can be referred to as a term used for summarizing an entire process used by an analyst to characterize a certain data sets. If this data set, is dependent on a sample consisting of a larger population, an analyst has to step up his or her game.

Analysts will be able to develop certain interpretations about an entire population based on a sample. Statistical analysis, itself will involve different processes of gathering data properly at first and then sending it for evaluation.

After this, data gets summarized into a mathematical form. One can make better business decisions when one has statistical data and conclusions in hand.

Usage of statistics

Statistics is often used in many disciplines, including psychology, social sciences, manufacturing firms etc. Gathering of all data is done by use of a sample procedure. There are two very popular methods used for analysis of data.

Descriptive statistics and inferential statistics, is used widely for data analysis. Descriptive statistics, is used for making synopsis of data from a certain sample. Procedures of mean or standard deviation is used for analyzing the data.

In inferential statistics, data is often viewed as a subclass of a particular population. Different methods are used in statistics to gather, analyze data and drawing final conclusions.

Different kinds of statistics

The mean, can be referred to as mathematical average of two or more numbers. Mean for a particular number set, can get calculated in many different ways. You can calculate arithmetic mean. It shows how a particular product or service has performed over time. By using geometric mean, performance of an investor’s portfolio, can be known. The investment might be in the same product over the same period of time as before.

Skewness and kurtosis deciphered

By skewness, you can come to know about the degree by which a data set varies from the standard distribution in a particular data set.

You will find that most of the data sets, which includes prices of stocks as well as commodities are positively skewed. The positive skew is on the left side of the data average. A negative skew is towards the right side of the data average.

By kurtosis, one comes to know whether a particular set of data has less outliers (light tailed) or is it more prone to outlier values (heavy tailed) than normal distribution. Different data sets, having high kurtosis, have heavy tails.

This implies occurrence of higher risks in your investment with a promise of occasional wild returns too. Data sets, having low kurtosis, have lighter tails or less outliers. This means, there would be less risks to investment here.

Regression and variance

With help of regression analysis, one can know the extent to which certain factors such as rate of interest or price of certain products can influence fluctuations in prices. These factors can be depicted in form of a straight line, which is known as linear regression. Variance can be depicted as span associated with particular set of numbers in data sets.

With help of variance, one can measure distance that a number in a set is, from the mean. With aid of variance, one can duly determine the kind of risk that an investor can accept while getting into an investment. Performance of different stocks at a time can be determined by it.

Stem and leaf plots discussed

With help of stem and leaf plot, one can analyze data as well as display it simultaneously. With help of this, each data value can be shown and its relationship with other values can be determined.

On turning a stem and leaf plot sideways, it looks like a histogram. The stem in this kind of plot is created by placing the biggest values on left side of a vertical line. The rest of the values are written on right of that line. These values are called leaves. Commonly, values in the stem are listed from smallest to greatest.

What are box plots?

Data in box and whisker plots are displayed in a really handy manner by breaking it down in four quartiles. In these quartiles, have equal number of values of data. One cannot see the frequency associated with the data in these plots.

You will also not be able to see individual statistics here. You can however very clearly see the position where the middlemost data value lies on. You can well understand the skewness of data using these plots.

There are certain quartiles such as Q1, Q2, Q3 present in these plots. The Q1 represent the median value present in the lower half of your data. Q2 is median value associated with whole data set and Q3 median of upper part of data set. The inter quartile range, is a value showing difference between Q1 and Q3. There are certain extreme values present in the data set too, these are the smallest and biggest value.

Scatter plots and correlation

Scatter plots are a great way to display data concerned with only two variables. Different predictions can also be made based on this data. These plots, show different individual values of data, something you cannot view in histograms or box plots. Relation between different variables can be achieved by using these scatter plots. This is known as correlation. There are basically three types of correlations.

  • In positive correlation, one variable increases along with the other.
  • In negative correlation, as one value increases, another falls.
  • In cases of no correlation, there exists no apparent relationship between variables.

Making use of line of best fit

By making use of line of best fit, one can make different predictions based completely on previous data. There exist many complex formulas, which can be used for exactly finding this line. People can also estimate it roughly.

The line that one draws through graphs, need to look, as if it fits into the trend of the data very well. When you are drawing line of best fit, you have to ensure that this line fits in with the maximum number of data points. If there exist some outliers, then those points are not required to be on your line.

Different events of probability

There are lots of events in probability that finds usage in statistics. For example, complementary events are those with only two outcomes. In case of mutually exclusive events, they occur independent of each other. These events cannot occur at the same time. You need to realize that all complementary events are mutually exclusive in nature, whereas the reverse is not always true. There are basically two distinct ways to calculate the probability. You can make use of math to predict the outcome. You may also actually observe different events and maintain a score.

You will see that theoretical probability, uses mathematics to predict outcomes of different events. Here you will be simply dividing number of possible outcomes with the number of possible ones. In experimental probability, any experiment or trial is observed. The total number of favorable outcomes are counted here and divided by the total number of times that the experiment was performed.

Simultaneously occurring events

In case of compound events, two or more number of things are occurring at the same time. People are usually concerned with the probability of things actually occurring and not how each are taking place individually over a period of time. There are many different ways to calculate these probabilities. You can make use of organized lists as well as tree diagrams to find desired results.

Using organized lists

Using this method, you will be actually listing out different possible outcomes that might have occurred. This process can prove to be a little difficult since there is always a probability of forgetting an option or two.

Applied statistics

Going through the basics of applied statistics, you will realize that there are certain techniques such as t-tests as well as correlation that can be used to find answers to real life questions. Emphasis is thoroughly given on different applications of these techniques and not the theory part.

Different concepts existing behind these techniques will obviously be explained. Stata is often used here for purpose of analysis. You will find that these software, are often preloaded into classroom devices.

You will be able to run basic statistical analysis quite easily using these techniques and also interpret the results you obtain. Techniques most suitable for certain researches can also be selected easily by this knowledge.

Going through regression

Students need to have basic knowledge of correlation as well as linear regression of the linear and multiple types. Attendants by going through this course will be able to read as well as interpret output associated with linear regression from commonly used packages of statistical software. Attendants, also have the chance of learning about linear regression analysis and when it is not appropriate to use with the data.

Things to know

Students wishing to enhance their knowledge of statistics, need to have an idea of the correct data type which is to be used during regression analysis. You need to know how lines of correlation and regression are related to each other. Interpretation of linear and multiple regression is very much required to be known here.

The validity of data used in linear regression, needs to be assessed thoroughly by students. In order to understand linear regression, you need to visualize the data very well. In multiple linear regression, there always exists categorical variables. You have to understand and interpret them properly.

Knowledge of mixed models

Students can learn about linear mixed models as well as generalized version of them. These regression models, possess random as well as fixed effects. Therefore, they are also known as linear models of hierarchy. These mixed models, are often run in commonly available statistical software.

Students come to know about mixed models and when they are to be used from here. Mixed models, are also used for analyzing longitudinal measures of data. You also need to have an idea of what to look for in the output and then interpret the results.

Different types of data and their measurements

In statistics, you will find that there are four data measurement scales present for students to use. These are namely, nominal, ordinal, ratio and interval based. Data can be further classified in different ways with the help of these scales.

Nominal scales are mostly used for labelling different variables which do not have a fixed value. These nominal scales are therefore simply called labels sometimes. The different scales seen here, are all mutually exclusive of each other. They simply do not have any kind of numerical significance.

Ordinal and interval scales

The order associated with different values is quite important for these scales. The difference between the values may not be known quite distinctly. Different non numeric things are measured with the help of these scales. Mode and median are often associated with this type of scale.  Order as well as difference between two values are known in case of interval scales. Many things can get covered within this scale. The difference between the interval scale and the ratio scale is that, the ratio scale has an absolute zero. Therefore, lots of possibilities can be explored with the help of these scales.

Author Bio

Michelle Johnson hailing from the University of Harvard, is a name always on the lips of her students. This is because of her excellent methods of teaching complex concepts associated with management and statistics. She is an MBA with over 6 years of experience in the sector. She is a well-known author, noted for the minutely analyzing different topics in her works.