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What is Statistics in Mathematics?

Statistics is a field of mathematics concerned with the study of data collection, analysis, interpretation, presentation, and organisation. Statistics is described as the process of gathering data, classifying it, displaying it in a way that is easy to understand, and analysing it further. Statistics is often defined as the process of drawing conclusions from a sample of data obtained through surveys or trials.

Statistics

Statistics is mostly used to acquire a better understanding of data and to focus on specific applications. The process of gathering, assessing, and summarising data into a mathematical form is known as statistics. Originally, statistics were associated with state science, in which they were used to gather and analyse facts and data about a country’s economy, population, and so on. Mathematical statistics uses tools such as linear algebra, differential equations, mathematical analysis, and probability theories. In mathematical statistics, there are two approaches for analysing data that are widely used: descriptive statistics and inferential statistics.

Descriptive Statistics

Using measures of central tendency and measures of dispersion, the descriptive technique of statistics is used to describe the data gathered and summarise the data and its attributes.

Inferential Statistics

This statistical strategy is used to generate inferences from data. Inferential statistics relies on statistical tests on samples to make inferences, and it does so by discovering differences between the two groups. This p-value is calculated in accordance to the probability of chance () = 0.05. If such p-value is less than or equal to, the p-value is considered significant statistically.

Data Representation in Statistics

A data set is a collection of observations and information. These facts and observations can be expressed as numbers, measures, or assertions. Qualitative and quantitative data are the two types of data available. When the data is explanatory or categorized, it is called qualitative data; when the data is numerical, it is called quantitative data. We want to depict the obtained data in several types of graphs such as a pie chart, bar graph, line graph, leaf and stem plots, scatter plot, and etc after we know the data gathering procedures. Anomalies that are caused to invariability un data readings are deleted before the data is analysed. Let’s take a look at the various types of data representation used in statistics.

  • A bar graph is a representation of a set of data using rectangular bars with lengths proportional to the values. The bars can be plotted either vertically or horizontally.
  • Pie Chart: A pie chart is a graph in which a circle is split into sectors, each representing a percentage of the total.
  • The data is represented as a sequence of points connected by a straight line in a line graph. These are referred to as markers.
  • Pictograph: A pictograph is a visual representation of data. Different numbers can be used to represent pictorial symbols for words, objects, or sentences.
  • Histogram: The histogram is a graph with rectangles in which the size is related to the occurrence of a statistic as well as the width is equivalent to that same class interval. 
  • Frequency Distribution:  In statistics, the frequency distribution table shows the data in ascending order with their associated frequencies. The frequency of data is frequently symbolised by the letter f.

Different Models of Statistics

Because statistics is such a broad term that it is used in so many different ways, different models of statistics are employed in different ways. A few models are listed below:

  • Skewness is a measurement of asymmetry in a probability distribution that quantifies the divergence of the standard normal distribution for data in stats. Skewed distributions can have a positive, negative, or zero value. When a curve changes from left to right, it is said to be skewed. Positive skewing occurs when the curve advances to the right, whereas left skewing occurs when the curve moves to the left.
  • ANOVA (Analysis of Variance) statistics – ANOVA stands for Analysis of Variance. The ANOVA statistics are the statistics used to calculate the mean difference for a given set of data. This statistical model is used to evaluate stock results over a given of time.
  • Degrees of freedom – When the values are altered, this statistical model is applied. The degree of freedom refers to the amount of data that may be shifted while estimating a parameter.
  • This statistical process defines the association between variables in the regression analysis model. When an independent variable changes, the process describes how a dependent variable change.

Measures of Central Tendency in Statistics

The cornerstone of descriptive statistics is the measure of central tendency and the measure of dispersion. The level of measurement that tells us where data points are centred is called the representative value for the given data. This one is done to see how the data is dispersed around the centred metric. To discover the core metrics of tendency, we employ the mean, median, and mode. We see the overall elevation of students, the average wealth, the typical exam result, or the average player height in our daily lives.

Solve this question: If 1-10, 11-20, 21-30, 31-40, ……., are the classes of a frequency distribution, then the upper boundary of the class 31-40 is?

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