all formulas of statistics class 11

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Frequently Used Statistics Formulas and Tables

Sample standard deviation for frequency table: = s n [ ∑ ( f • x 2 ) ] − [ ∑ ( f • x ) ] 2 n ( n − 1) Sample z-score: z = x − x s Population z-score: z −μ = x σ Interquartile Range: (IQR) = Q 3 − Q 1 Modified Box Plot Outliers lower limit: Q 1 - 1 5 (IQR) upper limit: Q 3 + 1 5 (IQR)

Why is it important to learn statistical techniques & formulas?
Being able to make the connections between those statistical techniques and formulas is perhaps even more important. It builds confidence when tackling statistical problems and solidifies your strategies for completing statistical projects.
What are the basic 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 order.
What is a statistic in mathematics?
Statistics is a branch of mathematics which deals with numbers and data analysis. Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. Statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample’s distribution.
How do you test a statistical hypothesis?
To test a statistical hypothesis, you take a sample, collect data, form a statistic, standardize it to form a test statistic (so it can be interpreted on a standard scale), and decide whether the test statistic refutes the claim. The following table lays out the important details for hypothesis tests.

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All Formulas of Statistics for Class 11

This tutorial covers all the essential formulas in statistics for Class 11 students. Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data. Understanding these formulas is crucial for solving statistical problems and interpreting data effectively.

4 examples

Practice Exercises

Below are some practice exercises to reinforce your understanding of the formulas:

Mean Calculation: Calculate the mean of the following data set: 12, 15, 18, 20, 22.
Standard Deviation: Find the standard deviation for the data set: 5, 8, 11, 14, 17.
Probability: Determine the probability of rolling a prime number on a fair six-sided die.
Hypothesis Testing: Perform a hypothesis test to determine if there is a significant difference in the mean scores of two groups.

Solutions:

Mean = (12 + 15 + 18 + 20 + 22) / 5 = 17.4
Standard Deviation = √[(Σ(x - μ)²) / N] = √[(5 + 0 + 9 + 36 + 81) / 5] ≈ 4.36
Probability of rolling a prime number = 3/6 = 0.5
Perform the appropriate statistical test (e.g., t-test) and interpret the results accordingly.

Subcategories Explanation

The subcategories of statistics for Class 11 include:

Descriptive Statistics: Involves organizing, summarizing, and presenting data.
Inferential Statistics: Involves making predictions or inferences about a population based on sample data.
Probability: Deals with the likelihood of events occurring.
Hypothesis Testing: Determines whether there is a significant difference between two groups or variables.

Notes

Here are some important notes to remember:

Understand the context of the problem before applying any statistical formula.
Always check the assumptions and conditions necessary for using a particular formula.
Interpret the results of statistical analyses in the context of the problem.
Regular practice is essential for mastering statistical concepts and formulas.

Step-by-Step Guide

Cases and Scenarios

Consider the following scenarios where statistical formulas are applied:

Business: Analyzing sales data to identify trends and make informed business decisions.
Healthcare: Studying the effectiveness of a new drug by comparing patient outcomes in the treatment and control groups.
Social Sciences: Conducting surveys to understand public opinion on various issues.
Environmental Science: Analyzing climate data to predict future weather patterns.

Questions and Answers

Here are some common questions related to statistics:

What is the difference between descriptive and inferential statistics?
Descriptive statistics involves summarizing and presenting data, while inferential statistics involves making predictions or inferences about a population based on sample data.
How do you calculate probability?
Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
What is hypothesis testing?
Hypothesis testing is a statistical method used to determine whether there is enough evidence to reject a null hypothesis.
Why is standard deviation important?
Standard deviation measures the dispersion of data points from the mean and helps assess the variability or spread of a data set.

Multiple Choice Questions

Test your understanding with the following multiple-choice questions:

What is the formula for calculating the median?
1. Sum of all values divided by the total number of values
2. Middle value of a sorted data set
3. Value that occurs most frequently in a data set
4. Range divided by two
Correct Answer: b. Middle value of a sorted data set
Which of the following is not a measure of central tendency?
1. Mean
2. Median
3. Mode
4. Variance
Correct Answer: d. Variance
What does a p-value indicate in hypothesis testing?
1. The probability of committing a Type I error
2. The strength of the relationship between two variables
3. The likelihood of observing the data if the null hypothesis is true
4. The margin of error in a confidence interval
Correct Answer: c. The likelihood of observing the data if the null hypothesis is true

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31 Measures of Central Tendency: Mode, Median, and - Cengage

Compute ∑x; that is, find the sum of all the data values 2 Divide the Because the formula for the population mean is the same as that for the Barron's Profiles of American Colleges, 19th Edition, lists average class size for introductory lec-