| The uncertainty and variation in different fields can be determined only through statistical analysis. These uncertainties are basically determined by the probability that plays an important role in statistics. Show
Table of Contents: What is Statistics?Statistics is simply defined as the study and manipulation of data. As we have already discussed in the introduction that statistics deals with the analysis and computation of numerical data. Let us see more definitions of statistics given by different authors here. According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”. According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”. Statistics – Download PDFDownload the PDF to get the statistics notes and learn offline too. Click here to Download Statistics PDFStatistics ExamplesSome of the real-life examples of statistics are:
Basics of StatisticsThe basics of statistics include the measure of central tendency and the measure of dispersion. The central tendencies are mean, median and mode and dispersions comprise variance and standard deviation. Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set. Variation is the measure of spread out of the collection of data. Standard deviation is the measure of the dispersion of data from the mean. The square of standard deviation is equal to the variance. Mathematical StatisticsMathematical statistics is the application of Mathematics to Statistics, which was initially conceived as the science of the state — the collection and analysis of facts about a country: its economy, and, military, population, and so forth. Mathematical techniques used for different analytics include mathematical analysis, linear algebra, stochastic analysis, differential equation and measure-theoretic probability theory. Types of StatisticsBasically, there are two types of statistics.
In the case of descriptive statistics, the data or collection of data is described in summary. But in the case of inferential stats, it is used to explain the descriptive one. Both these types have been used on large scale. Descriptive Statistics The data is summarised and explained in descriptive statistics. The summarization is done from a population sample utilising several factors such as mean and standard deviation. Descriptive statistics is a way of organising, representing, and explaining a set of data using charts, graphs, and summary measures. Histograms, pie charts, bars, and scatter plots are common ways to summarise data and present it in tables or graphs. Descriptive statistics are just that: descriptive. They don’t need to be normalised beyond the data they collect. Inferential Statistics We attempt to interpret the meaning of descriptive statistics using inferential statistics. We utilise inferential statistics to convey the meaning of the collected data after it has been collected, evaluated, and summarised. The probability principle is used in inferential statistics to determine if patterns found in a study sample may be extrapolated to the wider population from which the sample was drawn. Inferential statistics are used to test hypotheses and study correlations between variables, and they can also be used to predict population sizes. Inferential statistics are used to derive conclusions and inferences from samples, i.e. to create accurate generalisations. Statistics FormulasThe formulas that are commonly used in statistical analysis are given in the table below. \(\begin{array}{l}Sample\ Mean,\ \bar{x}\end{array} \) \(\begin{array}{l}\frac{\sum x}{n}\end{array} \) \(\begin{array}{l}Population\ Mean,\ \mu\end{array} \) \(\begin{array}{l}\frac{\sum x}{N}\end{array} \) \(\begin{array}{l}\sqrt{\frac{\sum (x-\bar{x})^{2} }{n-1}}\end{array} \) \(\begin{array}{l}Population\ Standard\ Deviation,\ \sigma\end{array} \) \(\begin{array}{l}\sigma = \sqrt{\frac{(x-\mu )^{2}}{N}}\end{array} \) \(\begin{array}{l}Sample\ Variance,\ s^{2}\end{array} \) \(\begin{array}{l}s^{2} = \frac{\sum (x_{i}-\bar{x})^{2}}{n-1}\end{array} \) \(\begin{array}{l}Population\ Variance,\ \sigma ^{2}\end{array} \) \(\begin{array}{l}\sigma ^{2} = \frac{\sum (x_{i} – \mu)^{2}}{N}\end{array} \) Range, (R)Largest data value – smallest data valueSummary StatisticsIn Statistics, summary statistics are a part of descriptive statistics (Which is one of the types of statistics), which gives the list of information about sample data. We know that statistics deals with the presentation of data visually and quantitatively. Thus, summary statistics deals with summarizing the statistical information. Summary statistics generally deal with condensing the data in a simpler form, so that the observer can understand the information at a glance. Generally, statisticians try to describe the observations by finding:
Summary Statistics Table The summary statistics table is the visual representation of summarized statistical information about the data in tabular form. For example, the blood group of 20 students in the class are O, A, B, AB, B, B, AB, O, A, B, B, AB, AB, O, O, B, A, AB, B, A. Blood GroupNo. of StudentsO4A4B7AB5Total20 Thus, the summary statistics table shows that 4 students in the class have O blood group, 4 students have A blood group, 7 students in the class have B blood group and 5 students in the class have AB blood group. The summary statistics table is generally used to represent the big data related to population, unemployment, and the economy to be summarized systematically to interpret the accurate result. Scope of StatisticsStatistics is used in many sectors such as psychology, geology, sociology, weather forecasting, probability and much more. The goal of statistics is to gain understanding from the data, it focuses on applications, and hence, it is distinctively considered as a mathematical science. Methods in StatisticsThe methods involve collecting, summarizing, analyzing, and interpreting variable numerical data. Here some of the methods are provided below.
What is Data in Statistics?Data is a collection of facts, such as numbers, words, measurements, observations etc. Types of Data
Types of quantitative data
Representation of DataThere are different ways to represent data such as through graphs, charts or tables. The general representation of statistical data are:
 A Bar Graph represents grouped data with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A type of graph in which a circle is divided into Sectors. Each of these sectors represents a proportion of the whole. The line chart is represented by a series of data points connected with a straight line. The series of data points are called ‘markers.’ A pictorial symbol for a word or phrase, i.e. showing data with the help of pictures. Such as Apple, Banana & Cherry can have different numbers, and it is just a representation of data. A diagram is consisting of rectangles. Whose area is proportional to the frequency of a variable and whose width is equal to the class interval. The frequency of a data value is often represented by “f.” A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies. Measures of Central TendencyIn Mathematics, statistics are used to describe the central tendencies of the grouped and ungrouped data. The three measures of central tendency are:
All three measures of central tendency are used to find the central value of the set of data. Measures of DispersionIn statistics, the dispersion measures help interpret data variability, i.e. to understand how homogenous or heterogeneous the data is. In simple words, it indicates how squeezed or scattered the variable is. However, there are two types of dispersion measures, absolute and relative. They are tabulated as below: Absolute measures of dispersionRelative measures of dispersion
Skewness in StatisticsSkewness, in statistics, is a measure of the asymmetry in a probability distribution. It measures the deviation of the curve of the normal distribution for a given set of data. The value of skewed distribution could be positive or negative or zero. Usually, the bell curve of normal distribution has zero skewness. ANOVA StatisticsANOVA Stands for Analysis of Variance. It is a collection of statistical models, used to measure the mean difference for the given set of data. Degrees of freedomIn statistical analysis, the degree of freedom is used for the values that are free to change. The independent data or information that can be moved while estimating a parameter is the degree of freedom of information. Applications of StatisticsStatistics have huge applications across various fields in Mathematics as well as in real life. Some of the applications of statistics are given below:
Video LessonGrade 11 StatisticsStatistics Related ArticlesAbsolute and Relative ErrorAlternative HypothesisAssumed Mean MethodBox and Whisker PlotCategorical DataCluster AnalysisConfidence IntervalControl ChartsCorrelation and RegressionArithmetic Mean And RangeData Collection And Organization Of DataMeasures of DispersionFrequency Distribution Table StatisticsInterpolationInterquartile RangeNull HypothesisP-valueQuartilesSample StatisticSampling ErrorTests of SignificanceZ-Score Table Hope this detailed discussion and formulas on statistics will help you to solve problems quickly and efficiently. Learn more Maths concepts at BYJU’S with the help of interactive videos. Frequently Asked Questions on StatisticsStatistics is a branch that deals with the study of the collection, analysis, interpretation, organisation, and presentation of data. Mathematically, statistics is defined as the set of equations, which are used to analyse things. The two different types of statistics used for analyzing the data are: What is Summary Statistics?Summary statistics is a type of descriptive statistics, which is used to summarize the set of observations with large information as simply as possible. Statisticians used to describe the observation by finding the measures of central tendency, statistical dispersion, statistical dependence, and the shape of the distribution. How is statistics applicable in Maths?Statistics is a part of Applied Mathematics that uses probability theory to generalize the collected sample data. It helps to characterize the likelihood where the generalizations of data are accurate. This is known as statistical inference. What is the purpose of statistics?Statistics make us learn to utilize a restricted sample to make accurate determinations about a more prominent populace. The utilization of tables, diagrams, and graphs assumes a crucial part in introducing the information being utilized to reach these determinations. What is the importance of Statistics in real life?Statistics encourages you to utilize legitimate strategies to gather the information, utilize the right examinations, and successfully present the outcomes. Measurement is a significant cycle behind how we make disclosures in science, settle on choices dependent on information, and make forecasts. What branch of mathematics is used to analyze data?Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory.
What branch of mathematics deal with the collection analysis and interpretation of numerical data to help in making more effective decisions?A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data is called statistics.
What is the branch of statistics that involves the collection organization summarization and interpretation of data?Descriptive statistics consists of the collection, organization, summarization, and presentation of data. In descriptive statistics the statistician tries to describe a situation. Consider the national census conducted by the U.S. government every 10 years.
Which type of statistics is used to organize and summarize data?Descriptive statistics summarize and organize characteristics of a data set. A data set is a collection of responses or observations from a sample or entire population.
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