Statistics XII Math Project.pdf
- 1. Statistics Submitted by- Pushpadant .R.Patil Submitted to- Venu Gopal Sir
- 2. What is Statistics? Statistics is a branch of mathematics that deals with the collection, review, and analysis of data. It is known for drawing the conclusions of data with the use of quantified models. Statistics can be defined as the study of the collection, analysis, interpretation, presentation, and organization of data. In simple words, it is a mathematical tool that is used to collect and summarize data.
- 3. Real-life examples of statistics are given below: ● To find the mean of the marks obtained by each student in a class of 40 students, the average value is the statistics of the marks obtained. ● Suppose you need to find the number of employed citizens in a city. If the city has a population of 10 lakh people, we will take a sample of 1000 people. Based on this, we can prepare the data, which is the statistic.
- 4. Basics of Statistics Statistics consist of the measure of central tendency and the measure of dispersion. These central tendencies are actually the mean, median, and mode and dispersions comprise variance and standard deviation. Mean is defined as the average of all the given data. Median is the central value when the given data is arranged in order. The mode determines the most frequent observations in the given data. Variation can be defined as the measure of spread out of the collection of data. Standard deviation is defined as the measure of the dispersion of data from the mean and the square of the standard deviation is also equal to the variance.
- 5. Mathematical Statistics The most common application of Mathematical statistics is the collection and analysis of facts about a country: its economy, and, military, population, number of employed citizens, GDP growth, etc. Mathematical techniques like mathematical analysis, linear algebra, stochastic analysis, differential equation, and measure-theoretic probability theory are used for different analytics.
- 6. Scopes Of Statistics Statistics can be used in many major fields such as psychology, geology, sociology, weather forecasting, probability, and much more. The main purpose of statistics is to learn by analysis of data, it focuses on applications, and hence, it is distinctively considered as a mathematical science.
- 7. Methods in Statistics The statistical process involves collecting, summarizing, analyzing, and interpreting variable numerical data. Some methods of statistics are given below. ● Data collection ● Data summarization ● Statistical analysis
- 8. What is Data in Statistics? Data can be defined as a collection of facts, such as numbers, word measurements, observations, quantities etc. Types of Data ● Qualitative data- it is a form of descriptive data. Example- She can write fast, He is tall. ● Quantitative data- it is in the form of numerical information. Example- An elephant has four legs.
- 9. Types of quantitative data ● Discrete data- it has a fixed value that can be counted ● Continuous data- it has no fixed value but has a range that can be measured. Collecting & Summarizing Data Data: A collection of observations, facts about an object is known as Data. Data can be in numbers or in statement/descriptive form.
- 10. Description of Data There are various ways to describe the data: Mode: Mode is the value that occurs very often in the list. It can be said that there is no mode value if no number is repeated in the list.
- 11. Median: Median is the middle value of the list. Median divides the list into two halves Mean: A mean is an average of all the numbers in the list. It can be calculated by adding up all the numbers and then dividing the sum by the number of values in the list.
- 12. Types of Statistics Being a broad term, there exist different models of statistics: Mean: A mean is an average of two or more numerals. Mean can be computed using Mathematical mean or Geometric mean. The mathematical mean shows how well the commodity performs over the period whereas the geometric mean shows the result of the investment of the same commodity over the same period. Regression Analysis: It is a statistical process that determines the relationship between variables. It is the process of understanding how the value of a dependent variable changes when any of the independent variables is changed.
- 13. kewness: Skewness is the measure of the distortion from the standard distribution in a set of data. A curve is said to be skewed if it is shifted to the left or to the right. If the curve is extended towards the right side, it is known as the positive skewed and if the curve is extended towards the left side, it is known as the left-skewed. Kurtosis: Kurtosis is the measure of the tailedness in the frequency distribution. Data set may have heavy-tails or light-tails. Variance: Variance in statistics is the measure of the data span. It is used to compare the performances of stocks over a period of time.
- 14. Representation of Data in Statistics There are various ways to represent data. For example- graphs, charts and tables. The general representation of statistical data is done with the help of: ● Bar Graph ● Pie Chart ● Line Graph ● Pictograph ● Histogram ● Frequency Distribution ● Venn Diagrams
- 15. Bar Graph: It is the rectangular bar representation of data. The bars can be horizontal or vertical. The length of the bar is proportional to the value that it represents. It represents data in the form of rectangular bars having length according to the values that they represent.
- 16. Pie Chart: It is also known as the Circle Graph as it uses sectors of the circle to represent the data. This graph is represented in the form of a circle which is divided into a various number of sectors where each sector represents a portion of the whole division.
- 17. Line Graph: A line graph is represented by the straight line which connects the data points. It is represented by a series of data points called markers. Usually, a line graph is used to represent the change of the data over the period of time.
- 18. Pictograph: It is the representation of the frequency of data using the symbols or pictures. A symbol can represent one or more numbers of data. It represents data with the help of pictures.
- 19. Venn Diagrams: It is the pictorial representation which contains a box along with circles. The box represents the Sample Space and the circles represent the events. There can be three types of Venn diagrams: a. Two or more than two separate circles (When there is no common data) b. Overlapping Circles (When some of the data is common) c. Circle within a circle (When the outer circle is the superset of the inner circle)
- 20. Histogram: It consists of rectangles Whose area is proportional to the frequency of a variable and whose width is equal to the class intervals.