September 3, 2024

**Overview: **Master CBSE Class 12 Applied Maths Inferential Statistics and learn to make educated predictions from sample data. This article covers the differences between descriptive and inferential statistics, essential for real-world applications and exam success in 2025.!

The Central Board of Secondary Education, often referred to as CBSE, has introduced a fresh elective course for Class 12 students studying Commerce. This new subject is named Applied maths statistics.

Now, for those of you wondering what this subject includes, think of it as diving deeper into real-world math applications that businesses and other sectors use. One significant area within this subject is Inferential Statistics.

Statistics, in its essence, is about understanding and working with numbers to make sense of vast amounts of data. Specifically, "Inferential Statistics" is a technique where we use a small set of data (a sample) to make educated guesses about a much larger group (a population).

This article aims to guide you through the nuances of this topic within the **CBSE Class 12 applied maths syllabus**, helping you grasp its importance and relevance in our data-driven world.

Inferential statistics is the process of using data analysis to understand the properties of an underlying distribution of **probability**. It takes data from a sample and makes inferences about the larger population from which the sample was drawn.

CBSE Class 12 Applied Maths Inferential Statistics curriculum consists of data-based case studies from the field of business, economics, psychology, biology, and census data is used to appreciate the power of data in contemporary society.

When we talk about statistics, we often encounter two main types: Descriptive and Inferential. Let's dive into what each of these terms means and how they differ from one another.

Imagine you took a survey of your classmates' heights. If you were to summarize this data, perhaps by calculating the average height, the tallest and shortest heights, or even by creating a graph that shows the distribution of everyone's heights, you'd be using descriptive statistics.

*Key Features of Descriptive Statistics:*

- It gives a straightforward overview or snapshot of the main aspects of the data.
- Common tools include averages (mean), measures of variability (standard deviation), and graphical representations (charts and histograms).
- Think of it as presenting raw data in a way that's easy to understand and share, without making any additional assumptions.

**Example**: In a class of 30 students, the average height is 5 feet 6 inches, with heights ranging from 5 feet to 6 feet 2 inches.

Now, let's say you wanted to use the height data from your class to make some guesses or predictions about the heights of all students in your school, or maybe even in schools across the country. This is where inferential statistics come into play.

*Key Features of Inferential Statistics:*

- It allows us to make educated guesses or inferences about a larger group using data from a smaller sample.
- It often uses probability theory to determine the likelihood of a particular outcome.
- While it provides deeper insights and predictions, there's always a degree of uncertainty.

**Example**: Based on the survey from one class, we might infer that most high school students' heights in the country range between 5 feet and 6 feet 2 inches. But, there's a chance this prediction could be off by a bit, since we haven't actually measured everyone!

While descriptive statistics simply describe and summarize data, inferential statistics go a step further to help us make predictions and inferences about larger populations based on the data from a smaller group. Think of descriptive statistics as the foundation, providing clear facts, while inferential statistics builds on this foundation to explore deeper insights and trends.

In the CBSE Class 12 Applied Maths curriculum, Inferential Statistics is listed in the Unit - 5. Here's a simple and detailed breakdown:

**What's This About?**

**Population:**It's the entire group we're interested in.**Sample:**A subset of that group.

**Key Points:**

**Population vs Sample:**Think of population as everyone in your school, and a sample as students from a single class.**Representative vs Non-Representative Sample:**A representative sample accurately reflects the larger group. It's like if you had a group of students that represents the overall performance of your school.**How to Draw Samples?****Simple Random Sampling:**Like picking names out of a hat.**Systematic Random Sampling:**Picking every 10th name from a list.

**Examples to Keep in Mind:**- Think of population data like the census or economic surveys.
- For a practical view, consider drawing more than one sample set from a single population.

**What's This About?**

**Parameter:**A value that tells something about the entire population.**Statistic:**A value that gives information about a sample.

**Key Points:**

**Parameter vs Statistic:**If a school's overall average grade is a parameter, then the average grade of one class is a statistic.**Understanding Statistical Significance:**It helps us know if the results from our sample can be applied to the larger population.**Central Limit Theorem:**Don't worry too much about the complex term! Just know it helps us understand large populations using smaller samples.

**What's This About?**

**Hypothesis:**An assumption or prediction you want to test.**Null vs Alternate Hypothesis:****Null Hypothesis:**A statement that assumes no effect or difference.**Alternate Hypothesis:**A statement that assumes there is an effect or difference.

**Key Points:**

**Degree of Freedom:**A fancy term that helps decide which t-table value we should look at.**Testing Hypothesis with t-Test:**It's a method to check if our assumption or prediction holds.**Examples:**- If you're trying to see if a new teaching method is effective, the null hypothesis might say it's not, while the alternate hypothesis says it is.

The inferential statistics topic holds a weightage of 6 Marks out of the **total 80 marks** in the question paper, which means it holds a 7.5% weightage of Class 12 CBSE Applied Maths Board Paper.

Subject |
Number of Periods |
Weightage |

Inferential Statistics | 10 | 06 |

Inferential statistics is an easy and scoring topic if studied with the correct approach and methodology. You can refer to some of the below-mentioned preparation tips to become more confident, and successful in inferential statistics.

- Develop an effective and time-efficient schedule for CBSE Class 12 Applied Math practicing Inferential statistics problems regularly.
- Go through with the conceptual meaning of the definition and then start practicing questions of statistics.
- Before starting questions on Inferential statistics, brush up on the fundamentals of descriptive statistics as some of its concepts will be used in the questions.
- Attempt solved examples and then solve the exercise questions to evaluate your knowledge about the concept.
- After studying all the subjects according to the latest syllabus and exam pattern, start your evaluation during which you need to solve the CBSE Sample Papers.

Inferential statistics is used in almost every branch of fields like social sciences, actuarial sciences, computer sciences, economics, business, medicine, demographic shifts, etc, or wherever we need to analyze a given set of data.

You can understand the importance of Inferential statistics by reviewing these daily life problems which are solved using inferential Inferential statistics concepts.

- A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false-positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
- In a national survey, 500 students are randomly selected from those taking applied maths and asked if applied maths is their favorite subject. 100 students reply that applied maths is their favorite subject. Give a 90% confidence interval for the proportion of all students taking applied maths who consider it their favorite subject.
- Suppose in a random sample of 225 undergraduate men at UMD that the average best (highest weight) bench press is 150 pounds, with a sample standard deviation of 20 pounds. Compute a 95% confidence interval for the average best bench press for UMD undergraduate men.

To help you get an idea about the type of questions that will be asked from the inferential statistics topic, we have provided few sample questions here.

Q) Suppose X1, . . . , X100 are i.i.d random variables which have uniform distribution on [a − 2, a + 2], where a is unknown. Suppose the random sample produces a sample mean equal to 3.

Compute a 95% confidence interval for a.

Q) In a mythical national survey, 225 students are randomly selected from those taking calculus and asked if calculus is their favorite subject. 100 students reply that calculus is their favorite subject. Give a 95% confidence interval for the proportion of all students taking calculus who consider it their favorite subject.

Q) Suppose in a random sample of 225 undergraduate men at UMD that the average best (highest weight) bench press is 150 pounds, with a sample standard deviation of 20 pounds. Compute a 95% confidence interval for the average best bench press for UMD undergraduate men.

Inferential Statistics in CBSE Class 12 Applied Maths offers students a profound opportunity to understand and apply statistical methods to real-world problems.

By focusing on this area, students not only prepare for their exams but also build foundational skills that are applicable across various professional fields.

- Real-World Application: Inferential statistics is crucial for translating sample data into general insights about larger populations, essential in fields like business, economics, and healthcare.
- Exam Importance: This topic carries significant weight in the CBSE Class 12 Applied Maths exam, emphasizing its academic importance.
- Conceptual Understanding: Students are encouraged to differentiate between descriptive statistics, which summarizes data, and inferential statistics, which makes predictions about a broader context.
- Practical Skills: Mastery of inferential statistics involves regular practice with real data sets, enhancing both analytical and problem-solving skills.
- Future Relevance: The skills gained from studying inferential statistics are not just for passing exams but are also invaluable in professional and academic pursuits post-schooling.

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