Statistics is a branch of mathematics that deals with the study of collecting, analyzing, interpreting, presenting, and organizing data in a particular manner. Statistics is defined as the process of collection of data, classifying data, representing the data for easy interpretation, and further analysis of data. Statistics also is referred to as arriving at conclusions from the sample data that is collected using surveys or experiments. Different sectors such as psychology, sociology, geology, probability, and so on also use statistics to function. Show
Mathematical StatisticsStatistics is used mainly to gain an understanding of the data and focus on various applications. Statistics is the process of collecting data, evaluating data, and summarizing it into a mathematical form. Initially, statistics were related to the science of the state where it was used in the collection and analysis of facts and data about a country such as its economy, population, etc. Mathematical statistics applies mathematical techniques like linear algebra, differential equations, mathematical analysis, and theories of probability. There are two methods of analyzing data in mathematical statistics that are used on a large scale:
Descriptive StatisticsThe descriptive method of statistics is used to describe the data collected and summarize the data and its properties using the measures of central tendencies and the measures of dispersion. Inferential StatisticsThis method of statistics is used to draw conclusions from the data. Inferential statistics requires statistical tests performed on samples, and it draws conclusions by identifying the differences between the 2 groups. Tests calculate the p-value that is compared with the probability of chance(α) = 0.05. If the p-value is less than α, then it is concluded that the p-value is statistically significant. Data Representation in StatisticsThe 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.
Different Models of StatisticsStatistics being a broad term used in various forms, different models of statistics are used in different forms. Listed below are a few models: Skewness - In statistics, the word skewness refers to a measure of the asymmetry in a probability distribution where it measures the deviation of the normal distribution curve for data. The value of skewed distribution could be positive or negative or zero. The curve is said to be skewed when it shifts from left to right. If the curve mores towards the right it is called a positive skewed and if the curve moves towards the left, it is called left-skewed. ANOVA Statistics - The word ANOVA means Analysis of Variance. The measure used in calculating the mean difference for the given set of data is called the ANOVA statistics. This model of statistics is used to compare the performance of stocks over a period of time. Degrees of freedom - This model of statistics is used when the values are changed. Data that can be moved while estimating a parameter is the degree of freedom. Regression Analysis - In this model, the statistical process determines the relationship between the variables. The process signifies how a dependent variable changes when an independent variable changed. Measures of Central Tendency in StatisticsThe measure of central tendency and the measure of dispersion are considered as the basis of descriptive statistics. The representative value for the given data is the measure of central tendency that gives us an idea of where data points are centered. This is done to find how the data are scattered around this centered measure. We use mean, median, and mode to find the central measures of tendency. In our day-to-day life, we find the average height of the students, the average income, the average score in exams, or of the player. The different measures of central tendency for the data are:
Mean, Median and Mode in StatisticsMean is considered the arithmetic average of a data set that is found by adding the numbers in a set and dividing by the number of observations in the data set. The middle number in the data set while listed in either ascending or descending order is the median. Lastly, the number that occurs the most in a data set and ranges between the highest and lowest value is the mode. For n number of observations, we have
Measures of Dispersion in StatisticsThe measures of central tendency do not suffice to describe the complete information about a given data. Thus we need to describe the variability by a value called the measure of dispersion. The different measures of dispersion are:
Mean Deviation For ungrouped dataIn statistics, the frequency distributions of data can be
discrete data or continuous. For n number of individual observations \(x_1, x_2, x_3, x_r, ..... x_n\), the mean deviation about mean and median are calculated as follows: Mean Deviation for Discrete Grouped dataThe measurements of the data units are clearly shown in such a frequency distribution. Let there be n distinct data points \(x_1, x_2, x_3, x_r, ..... x_n\), occurring with frequencies \(f_1, f_2, f_3.... f_n\). a) Mean deviation about mean
b) Mean deviation about median
Mean Deviation for Continuous Grouped dataHere the data points take any value within a range and they are continuous. They can be measured and represented by using intervals on the real number line. The frequency in which data are arranged in classes is not countable. a) Mean deviation about mean The mean of the continuous frequency distribution is centered at its mid-point in each class. Then the same procedure is followed as in the case of discrete frequency distribution. b) Mean deviation about median Median = \(l + \dfrac{\dfrac{N}{2}-C}{f}\times h\), where the median class is the class interval whose cf is ≥ N/2, N the sum of frequencies, l, f, h, and C are, the lower limit, the frequency, the width of the median class and C the cumulative frequency of the class just preceding the median class. After finding the median, |\(x_i\) - M| is obtained. Standard Deviation and VarianceWe have the other prominent methods in statistics to find the proper measure of dispersion, known as the variance and the standard deviation. While finding the mean deviation about the mean and the median, there arises a difficulty in taking squares of all the deviations.
Coefficient of VariationWe compare the coefficient of variations of two or more frequency distributions. This coefficient of variation in statistics is the ratio of the standard deviation to the mean, expressed in percentage. CV = σ/ \(\bar {x}\) × 100. The distribution that has a greater coefficient of variation has more variability around the central value than the distribution having a smaller value of the coefficient of variation. Important Notes
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Examples of Statistics
go to slidego to slidego to slide Great learning in high school using simple cues Indulging in rote learning, you are likely to forget concepts. With Cuemath, you will learn visually and be surprised by the outcomes. Book a Free Trial Class FAQs on StatisticsWhat is Statistics?Statistics is a branch of mathematics that deals with the study of collecting, analyzing, interpreting, presenting, and organizing data in a particular manner. It is referred to as arriving at conclusions of data with the use of data. What are the Two Types of Statistics?The two different types of statistics are: Descriptive Statistics: It is used to summarize the data and its properties using mean and standard deviation. What is Descriptive Statistics?Descriptive statistics describe the data features and provide summaries about the entire or sample population. We calculate the measures of central tendencies and measures of dispersion to summarize the data, in this type of statistics. What is Inferential Statistics?Inferential statistics predict and make inferences from the data is called inferential statistics. Many statistical tests are performed to arrive at conclusions. This inferential statistics has connections with probability and probability distribution. How is Statistics Used in Mathematics?Statistics is a part of applied mathematics that uses probability theory to simplify the sample data we collect. The concept of probability comes under statistics where we can determine if the data is true or false but mostly, the data is true. What is the Purpose of Statistics?Statistics helps in better understanding and accurate description. It also helps in proper planning in the statistical study. Finally, statistics uses tables, diagrams, and graphs as representing the information in a certain manner. What is the Importance of Statistics in Real Life?Statistics helps to utilize strategies to gather the information, examine them, 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 Are Examples of Statistics?We consider a class of students as a sample of the population of all the students in the school. We can calculate their average score in tests, their average height, weight etc based on the data collected. The required parameters are determined using the statistical measures are analyzed and interpreted further, as desired. For example, the scores of the students in the previous semester and this semester can be compared. What is the branch of mathematics that involves collecting organizing analyzing and interpreting data?Statistics is the branch of mathematics that studies the collection, organization, analysis and interpretation of numerical data.
Is a branch of mathematics that deals with the analysis and interpretation of numerical data in terms of samples and population?A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data is called statistics.
What are the 4 branches of mathematics?The main branches of mathematics are algebra, number theory, geometry and arithmetic.
What branch of science that deals with collecting organizing summarizing analyzing and making decisions from data?Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.
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