Statistics

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data.

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”.

Basics of Statistics

The 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 an 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 Statistics

Mathematical 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.

Scope of Statistics

Statistics 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

The methods involve collecting, summarizing, analyzing, and interpreting variable numerical data. Here some of the methods are provided below.

  • Data collection
  • Data summarization
  • Statistical analysis

Data

Data is a collection of facts, such as numbers, words, measurements, observations etc.

Types of Data-

  1. Qualitative data- it is descriptive data.
    • Example- She can run fast, He is thin.
  2. Quantitative data- it is numerical information.
    • Example- An Octopus is an Eight legged creature.

Types of quantitative data

  1. Discrete data- has a particular fixed value. It can be counted
  2. Continuous data- is not fixed but has a range of data. It can be measured.

Representation of Data-

Statistics- Bar graph Bar Graph
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.
Statistics-Pie chart Pie Chart
A type of graph in which a circle is divided into Sectors. Each of these sectors represents a proportion of the whole.
Statistics-Line graph Line graph
The line chart is represented by a series of data points connected with a straight line.
The series of data points are called ‘markers.’
Statistics-Pictograph Pictograph
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.
Statistics- Histogram Histogram
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.
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Frequency distribution in Statistics Frequency Distribution
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.

Formulas

Sample Mean (\(\bar{x}\)) \(\frac{\sum x}{n}\)
Population Mean (\(\mu\)) \(\frac{\sum x}{N}\)
Sample Standard Deviation (s) \(\sqrt{\frac{\sum (x-\bar{x})^{2} }{n-1}}\)
Population Standard Deviation (\(\sigma\)) \(\sigma = \sqrt{\frac{(x-\mu )^{2}}{N}}\)
Sample Variance (\(s^{2}\)) \(s^{2} = \frac{\sum (x_{i}-\bar{x})^{2}}{n-1}\)
Population Variance (\(\sigma ^{2}\)) \(\sigma ^{2} = \frac{\sum (x_{i} – \mu)^{2}}{N}\)
Range (R) Largest data value – smallest data value

Statistics PDF

Download the PDF to get the statistics notes and learn offline too.

Types of Statistics

Basically, there are two types of statistics.

  • Descriptive Statistics
  • Inferential 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 in large scale.

There is one more type of statistics, where descriptive is transitioned into inferential stats.

Skewness

Skewness, 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 Statistics

ANOVA 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 freedom

In 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

Some of the applications of statistic are given below:

  • Applied statistics, theoretical statistics and mathematical statistics
  • Machine learning and data mining
  • Statistics in society
  • Statistical computing
  • Statistics applied to mathematics or the arts

Statistics Examples

Some of the real-life examples of statistics are:

  • To find the mean of the marks obtained by each student in the class whose strength is 50. The average value here is the statistics of the marks obtained.
  • Suppose you need to find how many members are employed in a city. Since the city is populated with 15 lakh people, hence we will take a survey here for 1000 people (sample). Based on that, we will create the data, which is the statistic.

Statistics Related Articles

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 Statistics

What exactly is statistics?

Statistics 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 the things.

What are the two types of statistics?

The two different types of statistics used for analyzing the data are:

  • Descriptive Statistics: It summarizes the data form the sample using indexes
  • Inferential Statistics: It concludes from the data which are subjected to the random variation

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.

Test your knowledge on Statistics

7 Comments

  1. The members of a sport club, 60 male students, have their weights
    recorded, in pounds. The weights are given below:
    171 165 153 154 158 160 149 149 138 150
    131 174 147 155 160 140 156 156 174 153
    165 149 140 154 149 147 152 148 131 144
    153 155 132 149 169 160 169 160 136 154
    165 144 163 157 158 149 148 161 149 142
    160 139 149 145 147 158 150 171 167 144

    Construct the group frequency table to calculate the mean and standard
    deviation and compare them with the values obtained using the original
    ungrouped data.
    please solve this

  2. please also give information about arithmetic reasoning

  3. divyanka Tripathi

    Please solve……
    Fill in the blanks-
    (1) lower limit of the class interval 14- 22 is

  4. The content is fabulous,n very helpful thanks to the byjus.

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