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# Descriptive Statistics Review

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 Sub Topics Descriptive Statistic review helps in describing data in quantitatively form. Mean is the best descriptive form of the Descriptive Statistics .It is one of the most informative and accurate measure of the central tendency. Mean of the confidence interval data gives us a result value which is around the Mean and where the true mean value is located Descriptive Statistics provide simple summary about the data and the measures .They are very different from inferential statistics. Descriptive Statistics tells exactly what the data shows and it gives a manageable form of data with quantitative description .It is used in large group of data to give the result in a sensible way and helps to reduce the data in a simpler form It provide the historical details of the data as past details is useful in analyzing any Set of data .It shows patters and trends in a set of data and used to explore one variable for the time .It is analysis of data for the whole set of data. We can also define relationship between two variables with the help of Correlation and regression Types of Descriptive Statistics 1. Measure of Central Tendency’-It includes mean, median, mode 2. Measure of Dispersion –It includes Standard Deviation, skewness, minimum and maximum variable

## Statistics Overview

Statistics word has been derived from the word “status” which means in its original form as only the collection of the numerical data which was useful for a state. The initial statistical overview included the collection of taxes, distribution of land and collection of revenue. But now when we look at modern Statistics overview, there exist hardly any field where statistics is not used. It is used in science, business, economy and all other spheres of life. It is an essential part of almost every subject. We find the fundamental characteristics of statistics as follows:
1. Statistics is also expressed in form of Numbers, non quantitative words like poor, rich, honest, bad week have no representation in statistics, but they can be the analyzed words after the statistics calculations.
2. Statistics always work on the collection of data and it can never give conclusion based on individual cases.
3. The collection of the data in the statistics is done on the basis of pre- determined purpose.
4. The collected data is always interrelated and comparable to each other.
5. We need to maintain the standard of accuracy in order to get the correct predictions after the statistical calculations are done.
But there exist certain limitations on the data that it cannot study the qualitative figures like honesty, dedication, poverty and intelligence. Moreover statistics never work on the figures which are placed individually as it always deals with groups. Statistics laws cannot hold true on individual data. Another main problem of the study of statistics is that statistics data collected for one purpose cannot be suitable for any other purpose of the study. We have two types of data:
1. Primary Data and
2. Secondary Data.

## Graphical representation

While performing any statistical investigation, we need to collect the raw data. But the data that we collect in the original form is so huge and endless that we cannot come to any conclusions and predictions just by looking at it at a glance. We need to process it, arrange it in some desired order and use them for certain analysis. So we can say that we use the statistical techniques to collect, summarize, analyze, compare and interoperate the data to come to certain conclusions. This data arrangement can be in frequency table form, tally table form, in form of class mark or sometimes in form of graphical representation.

These days’ people spend lots of money in advertisement and publishing pictures. Most of the time we come across the data presented in form of graphs which gives the pictorial presentation to attract the customers to go for their particular product. These pictures show the benefits of buying a particular brand of car or scooter in compare to other brands, to use a particular brand of cosmetics in compare to other brands and even some times this graphic representation attract us to eat any particular brand products in comparison to other brands. Besides this we also see the graphical representation of data showing us to attract to buy any particular brand of the newspaper. These graphs are also used to view the election results time to time showing the status of different political parties in different regions.

The reason behind the graphical presentation of data is to look at the glance and come at certain conclusions and predictions instantly. We observe that common people do not take Interest in the numerical form of data or the predictions which come as the conclusion of that data. Person is instantly attracted towards the graphical presentation of the same data which is in form of different pictures for immediate analyzing of data. It helps in comparative study of the given data which is in Numbers. So with the purpose to convey the correct meaning, the Data Analysis chart must be properly titled and properly labeled. Different types of graphs can be drawn by which different types of data can be analyzed and give certain predictions. Some of the common methods of representing data through graphs are Bar charts, Histograms, polygons, pie charts, frequency curves and even plotting different graphs like temperature graph, sales of the week and other such data are presented by the graphs. There are many advantages of presenting the data in form of graphs.
If a graph is properly constructed, then graphs always show readily information which may be lost otherwise if the data is shown in form of the numerical data only.

It helps us to predict the trend in which the changes are occurring and the effects of these changes are observed and then further steps are taken which is the main aim of the Statistics, yes we do agree that the same data is also available in the form of table and can be used to come to certain conclusions, but every time, everyone is not so analytic to analyze the data and predict the right result from the available data.

The objectives of presenting the graphical presentation are as follows:
1. It helps us to view the complex data in the simpler form.
2. Graphs always help us to have an attractive, interesting and impressive view in compare to a table. All the special features of the data are visible at a glance and it becomes easy to view the rise and the down fall. It makes easy to look at the trends and the fluctuations that exist in the raw data which is rather impossible to look at, when the data is in the raw or even the tabular form.
3. It saves the time and the efforts of the statisticians as well as the observer to predict the results from the given graphs which are drawn with the help of data once collected.
4. The job of comparison becomes easy and simple by us of graphical presentation of data.
5. Every data conveys a message which becomes easy to understand with the help of the graph. A person who looks at the graph does not require any special knowledge of mathematics to understand it.

While drawing a simple graph following general rules must be remembered:
a. Proper title of the graph must be mentioned.
b. All independent variables must be represented on ‘X’ and ‘Y’ axis, which must always begin from (zero, zero) i.e. the origin of the graph.
c. Proper scale caption must be mentioned on ‘x’ and ‘y’ axis.
d. Suitable scale must be taken to draw the graph and then it should be mentioned on the top right corner of the graph.
e. Graph must be plotted neatly.

## Real world applications In Statistics

Statistics is widely used in modern times. At initial stage it was used to collect the information about public affairs, but gradually the use of Statistics has been extended in all scientific applications. We use statistics in every Sphere of life where mass of quantitative data is needed and its simplification and analysis is involved. Earlier it was used by the rulers to assess the military and the economic strength of their state. We use statistics.
In economics basically:
a. To formulate the economic laws based on the economic behavior.
b. To study economical problems like balance of trade, industrial growth, unemployment and problems related to national income and its wealth.
c. To deal with Complications of National Income Account and reading the statistics of National Balance sheets.
a. To take the decision related to the location and the size of the firm
b. To study the demand of the products produced or sold by your organization.
c. For the production planning
d. For quality control and maintaining the stock.
e. For planning of marketing decisions and the strategies to be adopted.
f. For planning the future operations like capital investments and the equipments required by the company. It helps in the forecast about the sale, prices and the profit or loss expected in the future.
g. In Inventory control, for coordinating production and sale .
h. For operation research of the business.
i. For keeping track on the business accounts and auditing
Besides this statistics is used in several other areas like it has a major role in stocks and shares to predict the rise and fall in the market, based on which the share market runs. Statistics also plays a major role in the study done by insurance companies, brokers and even by the bankers.

## Descriptive Analysis and Single Variable Data

When a large amount of data or observations are summed up together to produce some statistical output is termed as descriptive Data Analysis. It helps us to produce the summary of the data. It gives us the simple summary about the sample of data collected and the measures to be taken on that data. Whenever we need to describe a large amount of data with a single variable, then it is termed as single variable data analysis.
Suppose we have collected the data of all the students who have performed in an annual examination and their Percentage is collected. Thus if a child scores 95% marks, it represents that the child is academically strong , on the another hand, if the child scored 42% marks gives the analysis that the child needs to put more efforts in academics. Similarly the GPA (the Grade Point Average) of the student is the single variable, introduced in schools, which makes the analysis of the academic performance of the child in single figure. It helps us to analyze and describe the data which is a good managerial tool and a large number of people can be put and measured using this measurement scale. It describes the basic feature which the complete data possess.

## Linear Correlation

Linear correlation is a widely used to measure the strength of relation between two variables in Statistics. For this it uses a Correlation Coefficient. The Correlation Coefficient is basically a coefficient which shows the strength of association of data or flow of data between two variables. The linear correlation statistics is used to find the linear association between two or more variables and; for this it uses Pearson product moment correlation coefficient. In this whole paper correlation coefficient is represented by Pearson product moment correlation coefficient. A correlation coefficient is calculated for any sample of data is denoted as S (r), and the correlation coefficient calculated for a population can be represented by either symbol ‘ε’ or s(R).
To interpret a statistics Linear Correlation Coefficient sign and the absolute value is used which shows the direction of the relation as well as magnitude also. Here are some important points related to Linear Correlation Coefficient:
1. The value of correlation coefficient always lies between -1 to 1.
2. For a stronger linear correlation the absolute value must be greater.
3. The strongest and best correlation is shown by coefficient of 1 or -1.
4. For a weakest correlation the coefficient is always a zero.
5. Positive correlation means if we increase the value of one variable then other’s value also increases.
6. Negative correlation means if value of one variable increases then the other’s value decreases.
For showing the Linear Correlation Scatter Plots are used to represent the different Patterns of the degree of correlation between two variables. When the Slope of any line is given by a negative value that means that correlation is negative and similarly if Slope of the line is positive then the correlation is positive. When all the data points exist on an exact straight path or line that means there is a strongest correlation between variables. The Linear Correlation becomes weakest as the data points become scattered on the plot i.e. not in a Straight Line. If all the data points are randomly scattered (without any pattern) then correlation does not exist between variables. Outliers are the data points which do not fall on the straight path or line. These outliers affects the correlation means these outliers reduces the strength of correlation.
Formula to calculate the linear correlation coefficient of a sample:
S = ∑ (p*q) / √(∑p2) (∑q2),
Here ‘S’ is the sample of data and symbol ‘∑’ is for summation and ‘p’ is (pi - p) and similarly q is (qi - q); ‘p’ and ‘q’ are the Mean value of all the data points of the sample and pi, qi are the i th value of observation.
Formula to calculate the linear correlation coefficient of a population:
s or ε = [1/N] ∑ [(pi - µp) / σp] [(qi - µq) / σq],
Here total Numbers of observations are denoted by ‘N’ and ‘σp’ and ‘σq’ are Standard Deviation of ‘p’ and ‘q’ respectively. ‘∑’ is a symbol of summation and ‘pi’ and ‘qi’ represents the I th value of the observation and ‘µp’, ‘µq’ are population mean.

## Probabilities

Probabilities in Statistics can be defined as the possibility of occurrence of any event. Now let us look at statistics Probability in details:
In case of tossing coin, there is a possibility of getting either head or tail on tossing. It means that there are two possibilities. The possibility of getting a head is ½ and the possibility of getting a tail is also ½.
We also observe that the sum of all possible outcomes of any experiment is always 1.Here ½ + ½ = 1
Probability can be calculated as = number of favorable outcomes / total number of possible outcomes.
Let us consider another example of rolling a dice. The possible outcomes of rolling a dice are 1, 2, 3, 4, 5, 6. So total number of outcomes are 6. If we look at the probability of following events:
Probability (Getting a even number). We see that we have 2, 4, 6 as the even Numbers.
So, P (Even Number) = 3/6
Similarly P (Odd Number) = 3/6
P (getting a number less than 5) = It includes all the numbers less than 5, i.e. 1, 2, 3, 4. (The possible outcomes are 4)
So P (getting a number less than 5) = 4 / 6 = 2/ 3
Probability statistics includes the study of different types of probability. We see that the value of probability varies between 0 and 1 (inclusive of both sides). We can divide the events in different classes based on the probability.
Impossible Event: Any event is called impossible if we find that its probability statistics is Zero (0). Let us consider an example of picking a card from a pack of 52 cards excluding jokers. Now what is the probability of getting a Joker.
We know that joker does not exist in the pack of cards, so the probability of getting the joker is zero, so we write-
P (Joker) = 0 / 52. Such an event is called an Impossible Event.
Other example of impossible event is getting number 7 on rolling a dice.
Sure event: A statistical probability of getting the value 1 is called Sure Event. Let us consider any event of throwing a dice.
What is the possibility of getting a natural number less than equal to 6. On every throw, the number we get will be less than or equal to six, so the probability is 1. Such events are called sure events or certain event.
Low probability and high probability events: The events which have the probability near to zero are called low probability statistics and the events which have the probability inclined towards 1 are called high probability events.
If the probability of any event is not affected by the previous events, then such events are called Independent Events, on other hand, if probability of any event is affected by the previous events are called dependent events. Tossing of a coin is an independent event and taking out two cards, one after another is called dependent event, as when we take out the second card after the first card is taken out from the pack, that time there are only 51 cards in the pack.