CBSE Class 10th Median of Grouped Data Details & Preparations Downloads
Welcome to the world of statistics, where numbers tell stories and patterns reveal themselves. In this blog, we'll embark on a mathematical journey to understand a key measure of central tendency – the median – specifically when dealing with grouped data. So, let's dive into the realm of Class 10 Math and explore the intricacies of finding the median in grouped data sets.
Unlocking Statistical Mastery: CBSE NCERT Download Guide to Mastering the Median of Grouped Data
What is the Median?
The median is a statistical measure that represents the middle value of a dataset. It's the point where half of the data lies below and half lies above. While finding the median for individual or raw data is straightforward, dealing with grouped data requires a nuanced approach.
Understanding Grouped Data:
Grouped data is organized into intervals or groups, making it more manageable for analysis. Each interval represents a range of values, and the data points within each interval are summarized using frequency distributions.
Calculating Median for Grouped Data:
Finding the median for grouped data involves identifying the median class, which is the interval containing the median. To determine the exact median, we use a formula that incorporates the lower boundary of the median class, cumulative frequency, and class width.
What is Median of Grouped Data?
The genric meaning of median, i.e. the middle value corresponding to a given distribution, remains same in this case too. As we have data in form of intervals (classes) in this case, we have a corresponding median class to find the value of median.
Also, we need to define cumulative frequencies for each class, which is a kind of prefix sum of frequencies of classes taken in order. The median value lies between the lower limit and upper limit of the median class. This value can be used by using a specified formula discussed as follows.
What is Median?
Median is a value corresponding to the middlemost data point in a dataset, when arranged in ascending order. The value of median helps one to know about center of a dataset. On comparing the value of median with that of mean, one can get idea of distribution of values in a dataset.
To find median of ungrouped data, one can simply sort the data points in ascending order. In case of odd number of observations, the middle value would be the median. On the other hand , for even number of observations, one can take mean of the two middle values to find the median. But there is a different method to find median of grouped data discussed later in this article.
Median of Grouped Data Formula
We can use the following formula to calculate median of grouped data:
Median = l + ((n/2-cf)/f)×h
Where,
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l is the lower limit of the median class,
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n is the total number of observations,
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cf is the cumulative frequency of the class preceding median class,
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f is the frequency of the median class, and
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h is the class size (upper limit – lower limit).
The steps listed below illustrate the procedure to find median of grouped data.
How to Calculate Median of Grouped Data?
The steps followed to calculate median of grouped data are discussed as follows:
Step 1: First, we find out the total number of observations by summing up all the frequencies.
Step 2: Then, we need to find the median class, i.e. the class having cumulative frequency just greater than half of total number of observations.
Step 3: Now, we note the values of lower limit of median class (l), frequency of the median class (f), cumulative frequency of the class preceding median class (cf), and class size (h).
Step 4: Next, we can substitute these values in the formula to calculate median of grouped data, i.e.
Median = l + ((n/2-cf)/f)×h
Solved Examples on Median of Grouped Data
Example 1: Calculate the value of median for the following data distribution:
Class Interval |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
Frequency |
5 |
7 |
12 |
10 |
6 |
Solution:
To find the median of given data, we build a table containing cumulative frequencies for each class interval along with the frequencies.
Class Interval |
Frequency (f) |
Cumulative Frequency (cf) |
0-10 |
5 |
0+5 = 5 |
10-20 |
7 |
5+7 = 12 |
20-30 |
12 |
12+12 = 24 |
30-40 |
10 |
24+10 = 34 |
40-50 |
6 |
34+6 = 40 |
Here, the total number of observations are 40, i.e. n = 40. We have, n/2 = 20, now the class having cumulative frequency just greater than or equal to 20 is the class interval 20-30 (cf = 24).
Thus, the median class is 20-30. Also, here the value of class size (h) is 10 (upper limit – lower limit). The lower limit (l) and frequency (f) of the median class are 20 and 12 respectively. And, the cumulative frequency (cf) of class preceding the median class is 12. Now, we can substitute these values in the formula to calculate value of median,
Median = l + ((n/2-cf)/f)×h
= 20 + ((20-12)/12)×10
= 20 + (8/12)×10
= 20 + 6.67
Median = 26.67
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 median, and why is it a crucial measure of central tendency in statistics?
Answer: The median is the middle value of a dataset. It's crucial as it provides a representative measure, unaffected by extreme values.
Q2 How does dealing with grouped data impact the calculation of the median compared to raw data?
Answer: Grouped data requires identifying the median class and using a specific formula, considering cumulative frequency and class width for accurate calculation.
Q3 What role does the cumulative frequency play in finding the median of grouped data?
Answer: Cumulative frequency is essential; it helps locate the median class and facilitates precise calculation using the median formula.
Q4 Can you explain the significance of the lower boundary in the median calculation for grouped data?
Answer: The lower boundary is crucial; it anchors the calculation, ensuring accuracy when determining the exact position of the median within the median class.
Q5 How does the median formula for grouped data accommodate different datasets with varying class widths?
Answer: The formula incorporates the class width, ensuring adaptability to different datasets and providing a standardized method for median calculation.