CBSE Class 10th Mode of Grouped Data Details & Preparations Downloads
Mathematics is not just about numbers; it's about finding patterns, making sense of data, and drawing meaningful conclusions. One such statistical measure that helps us uncover patterns in a set of data is the mode. In this blog, we will delve into the fascinating world of the mode, focusing specifically on its application to grouped data. So, fasten your seatbelts as we embark on a mathematical journey to demystify the mode of grouped data.
Unlocking Statistical Insights: CBSE NCERT Download on Mode of Grouped Data Demystified
What is Mode?
Before we dive into the mode of grouped data, let's refresh our memory on what mode is. In statistics, the mode is the value that appears most frequently in a dataset. It is a measure of central tendency that helps us identify the most common observation.
Understanding Grouped Data:
Grouped data, unlike individual or raw data, is organized into intervals or groups. This is often done to simplify large datasets and make them more manageable. Each interval represents a range of values, and the data points within each interval are summarized using a frequency distribution.
Calculating Mode for Grouped Data:
Now, let's explore how to calculate the mode for grouped data. The mode can be found using the modal class, which is the interval with the highest frequency. To determine the mode precisely, we can use a formula that incorporates the modal class, the class width, and the frequencies of the adjacent classes.
How to Find the Mode of Grouped Data?
In the case of grouped data, it is not possible to identify the mode of the data, by looking at the frequency of data. In this scenario, we can determine the mode value by locating the class with the maximum frequency called the modal class. Inside a modal class, we can locate the mode value of the data by using the formula,
f1 is the frequency of the modal class
f0 is the frequency of the class preceding the modal class
f2 is the frequency of the class succeeding the modal class
h is the size of the class intervals
Mode of Grouped Data Example
Question:
A survey has been conducted by a group of students on 20 households in a locality as shown in the following frequency distribution table. Find the mode for the given data.
Size of Family |
1-3 |
3-5 |
5-7 |
7-9 |
9-11 |
No. of Families |
7 |
8 |
2 |
2 |
1 |
Solution:
From the given table, it is observed that the maximum class frequency is 8, and the corresponding class interval is 3-5.
Therefore, the modal class for the given data is 3-5.
The lower limit of modal class, l = 3
Class size, h = 2
Frequency of modal class, f1 = 8
Frequency of class proceeding to modal class, f0 = 7
Frequency of class succeeding to modal class, f2 = 2
We know that the formula to find the mode of the grouped data is:
Mode = 3 + (2/7)
Mode = (21+2)/7
Mode = 23/7
Mode = 3.286.
CBSE Class 10th Downloadable Resources:
1. CBSE Class 10th Topic Wise Summary | View Page / Download |
2. CBSE Class 10th NCERT Books | View Page / Download |
3. CBSE Class 10th NCERT Solutions | View Page / Download |
4. CBSE Class 10th Exemplar | View Page / Download |
5. CBSE Class 10th Previous Year Papers | View Page / Download |
6. CBSE Class 10th Sample Papers | View Page / Download |
7. CBSE Class 10th Question Bank | View Page / Download |
8. CBSE Class 10th Topic Wise Revision Notes | View Page / Download |
9. CBSE Class 10th Last Minutes Preparation Resources (LMP) | View Page / Download |
10. CBSE Class 10th Best Reference Books | View Page / Download |
11. CBSE Class 10th Formula Booklet | View Page / Download |
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SAMPLE PRACTICE QUESTION
Q1 What is the mode of grouped data, and how does it differ from the mode of raw data?
Answer: The mode of grouped data is the value or interval with the highest frequency in a grouped dataset. It differs from raw data mode as it deals with data organized into intervals or groups.
Q2NWhy is grouped data used in statistics, and how does it impact the calculation of the mode?
Answer: Grouped data is used to simplify large datasets, making them more manageable. In mode calculations, the modal class (interval with the highest frequency) is crucial in determining the mode for grouped data.
Q3 Can you explain the significance of the modal class in calculating the mode of grouped data?
Answer: The modal class is the interval with the highest frequency in grouped data. It is essential in mode calculations, as a key component in the formula to precisely determine the mode.
Q4 What challenges might arise when working with grouped data, and how can they be addressed in mode calculations?
Answer: Challenges in grouped data may include loss of precision. To address this, statisticians use the modal class, class width, and frequencies of adjacent classes in the mode formula to make accurate calculations.
Q5 How is the mode of grouped data calculated using the CBSE NCERT approach?
Answer: The mode of grouped data using the CBSE NCERT approach involves identifying the modal class and applying a specific formula that incorporates the class boundaries, frequencies, and class width.