CBSE Class 10th Statistics Details & Preparations Downloads

Statistics, a branch of mathematics, plays a pivotal role in understanding and interpreting data. As Class 10 students embark on their journey through mathematics, the study of statistics becomes a key component. In this blog post, we will explore the fundamental concepts of statistics, providing a solid foundation for Class 10 students.

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I. Understanding the Basics:

Statistics involves the collection, analysis, interpretation, presentation, and organization of data. Class 10 students will delve into the fundamental terms and concepts, such as mean, median, mode, and range. These tools serve as the building blocks for more advanced statistical analyses.

II. Data Representation:

One of the crucial aspects of statistics is the ability to represent data visually. Graphs and charts, including bar graphs, histograms, and pie charts, become essential tools for conveying information effectively. Class 10 students will learn to choose the most appropriate representation for different types of data.

III. Measures of Central Tendency:

Class 10 introduces students to measures that describe the center of a data set. Understanding mean, median and mode helps in summarizing data and gaining insights into the typical or central values.

Ungrouped Data

Ungrouped data is data in its original or raw form. The observations are not classified into groups.

For example, the ages of everyone present in a classroom of kindergarten kids with the teacher are as follows:

3, 3, 4, 3, 5, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 27.

This data shows that there is one grown-up person present in this class, and that is the teacher.  Ungrouped data is easy to work with when the data set is small.

Important Relations Between Methods of Finding Mean

• All three methods of finding mean yield the same result.
• Step deviation method is easier to apply if all the deviations have a common factor.
• Assumed mean method and step deviation method are simplified versions of the direct method.

Median

Finding the median of grouped data when class intervals are not given

Step 1: Tabulate the observations and the corresponding frequency in ascending or descending order.

Step 2: Add the cumulative frequency column to the table by finding the cumulative frequency up to each observation.

Step 3: If the number of observations is odd, the median is the observation whose cumulative frequency is just greater than or equal to (n+1)/2

If the number of observations is even, the median is the average of observations whose cumulative frequency is just greater than or equal to n/2 and (n/2)+1.

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Grouped Data

In grouped data, observations are organized in groups.

For example, a class of students got different marks in a school exam. The data is tabulated as follows:

This shows how many students got the particular mark range. Grouped data is easier to work with when a large amount of data is present.

Frequency

Frequency is the number of times a particular observation occurs in data.

For example, if four students have scored marks between 90 and 100, then the marks scored between 90 and 100 have a frequency of 4.

Class Interval

Data can be grouped into class intervals such that all observations in that range belong to that class.

Class width = upper class limit – lower class limit

Example: Consider a class interval 31 – 40.

Here, the lower class limit is 31, and the upper class limit is 40.

Hence, the size/width of the class interval 31 – 40 is calculated as follows:

Class interval size = Upper class limit – Lower class limit

Class interval size = 40 – 31 = 9

Therefore, the size of the class interval is 9.

Direct Method to Find Mean

Step 1: Classify the data into intervals and find the corresponding frequency of each class.

Step 2: Find the class mark by taking the midpoint of the upper and lower class limits.

Step 3: Tabulate the product of the class mark and its corresponding frequency for each class. Calculate their sum (∑xifi).

Step 4: Divide the above sum by the sum of frequencies (∑fi) to get the mean.

Assumed Mean Method to Find Mean

Step 1: Classify the data into intervals and find the corresponding frequency of each class.

Step 2: Find the class mark by taking the midpoint of the upper and lower class limits.

Step 3: Take one of the xi’s (usually one in the middle) as the assumed mean and denote it by ′a′.

Step 4: Find the deviation of ′a′ from each of the x′is
di=xi−a

Step 5: Find the mean of the deviations

Step 6:  Calculate the mean as

For example, let us consider the same example as provided above.

In this method, first, we have to choose the assumed mean (a), which lies in the centre of x₁, x₂, …x_n. Here, we choose a = 47.5.

Secondly, we have to find the difference(di), which is obtained using the formula, 

d_i = x_i – a 

Cumulative Frequency Distribution of Less Than Type

The cumulative frequency of the less than type indicates the number of observations which are less than or equal to a particular observation.

Cumulative Frequency Distribution of More Than Type

A cumulative frequency of more than type indicates the number of observations that are greater than or equal to a particular observation.

Mode

In statistics, the mode is the most repeated value in the given data set. In other words, the data with the highest frequency is called the mode.

For example, 4, 12, 5, 6, 5, 8, and 5 are the given set of data.

Here, the data with the highest frequency is 5, which is repeated thrice.

Therefore, the mode of the given data is 5.

Finding mode for grouped data when class intervals are not given

In grouped data without class intervals, the observation having the largest frequency is the mode.

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Finding Mode for Ungrouped Data

For ungrouped data, the mode can be found out by counting the observations and using tally marks to construct a frequency table.
The observation having the largest frequency is the mode.

Finding mode for grouped data when class intervals are given

For grouped data, the class having the highest frequency is called the modal class. The mode can be calculated using the following formula. The formula is valid for equal class intervals and when the modal class is unique.
Mode = l + [(f1 – f0)/(2f1 – f0 – f2)] × h

Where,
l = lower limit of modal class
h = class width
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeeding the modal class.

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CBSE Class 10th Downloadable Resources: 

Being in CBSE class 10th and considering the board examinations you must be needing resources to excel in your examinations. At TestprepKart we take great pride in providing CBSE class 10th all study resources in downloadable form for you to keep you going. 

Below is the list of all CBSE class 10th Downloads available on TestprepKart for both Indian and NRI students preparing for CBSE class 10th in UAE, Oman, Qatar, Kuwait & Bahrain. 

FAQ

Q1: What is the significance of data presentation in statistics?

Ans: Data presentation in statistics is crucial as it helps in understanding patterns, trends, and variations within a dataset. Graphical representation and summary statistics make complex information more accessible.

Q2: Can you explain the difference between grouped and ungrouped data?

Ans: Ungrouped data refers to raw data without any categorization, while grouped data is organized into intervals or classes, making it easier to analyze and interpret.

Q3: How are measures of central tendency, like mean and median, calculated and applied in statistics?

Ans: The mean is calculated by summing up all values and dividing by the total number. The median is the middle value when data is arranged in ascending or descending order. These measures help represent the central value of a dataset.

Q4: What role do histograms and frequency polygons play in statistical representation?

Ans: Histograms and frequency polygons are graphical representations used to display the distribution of data. They provide insights into the shape, center, and spread of the dataset.

Q5: How does the concept of cumulative frequency enhance data analysis?

Ans: Cumulative frequency is the sum of frequencies up to a certain point in a dataset. It aids in constructing cumulative frequency distributions and understanding the overall distribution of the data.