Marks obtained No. of students 25 5 30 6 35 3 40 1
Calculating Mean Marks for a Frequency Distribution
The question asks us to find the average (mean) marks obtained by students based on the provided frequency distribution. A frequency distribution shows how often each value (in this case, marks) occurs.
Understanding the Mean Formula
To calculate the mean of a frequency distribution, we use the following formula:
\( \text{Mean} = \frac{\sum (f \cdot x)}{\sum f} \)
Where:
- \(x\) represents the individual values (Marks obtained).
- \(f\) represents the frequency of each value (No. of students).
- \(\sum (f \cdot x)\) is the sum of the products of each mark and its corresponding frequency.
- \(\sum f\) is the total number of observations (total number of students).
Step-by-Step Calculation
First, let's create a table to organize the data and calculate the product \(f \cdot x\) for each row.
| Marks obtained (\(x\)) | No. of students (\(f\)) | Product (\(f \cdot x\)) |
|---|---|---|
| 25 | 5 | \(25 \times 5 = 125\) |
| 30 | 6 | \(30 \times 6 = 180\) |
| 35 | 3 | \(35 \times 3 = 105\) |
| 40 | 1 | \(40 \times 1 = 40\) |
Next, we sum the frequencies (\(\sum f\)) and the products (\(\sum (f \cdot x)\)).
- Total number of students: \( \sum f = 5 + 6 + 3 + 1 = 15 \)
- Sum of the products: \( \sum (f \cdot x) = 125 + 180 + 105 + 40 = 450 \)
Finding the Mean Marks
Now, we apply the mean formula using the calculated sums:
\( \text{Mean} = \frac{\sum (f \cdot x)}{\sum f} = \frac{450}{15} \)
\( \text{Mean} = 30 \)
Therefore, the mean marks obtained by the students in this distribution is 30.
Similar Questions
- The Table given below represents the ages of students in a private music school. What is the average age of the students?
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Important Questions from Average
- The average of first 169 even numbers is
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- The average of first 152 odd natural numbers, is:
The average runs scored by a batsman in 23 matches is 40. In the next 10 matches, the batsman scored an average of 16 runs. Find his average runs scored (rounded off to two decimals) in all the 33 matches.
- The sum of five numbers is 655. The average of the first two numbers is 80 and the third number is 101. Find the average of the remaining two numbers.
