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 median of the observations 4, 14, 11, 8, 7, 8, 9, 12, 4, and 6 is:
The weights (in kg) of 9 members of a school cricket team are 50, 63, x, 62, 64, 48, 51, 55, 48. If the mean weight is 56 kg, then the value of x is:
A group of people consists of men, women, and children. 40% of them are men, 35% are women, and the rest are children, and their average weights are 70 kg, 60 kg, and 30 kg, respectively. The average weight of the group is:
If the mean of 22, 25, 27, 24, and x is 26, then the value of x is:
The average of the first 30 natural numbers is:
The average of the first twelve multiples of 11 is:
The average of 10 observations is 46. It was realised later that an observation was misread as 42 in place of 142. Find the correct average.
The average of the prime numbers between 11 and 30, both excluded, is:
The average of 70 values is 40. If each value is multiplied by 20, what will be the changed average?
- A class of 30 students appeared in a test. The average score of 12 students is 68, and that of the rest is 70. What is the average score of the class?
Important Questions from Average
Average of 40 numbers is 71, if the number 100 replaced by 140, then average is increased by
The captain of a football team of 11 members is 28 years old and the goalkeeper is 4 years older than him. If the ages of these two are removed, then the average age of the remaining players is two years less than the average age of the whole team. What is the average age of the team?
There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.
Consider the following statements:
1. The average score of Class-B will definitely decrease.
2. The average score of Class-A will definitely increase.
Which of the above statements is/are correct?
The average weight of A, B, Cis 40 kg, the average weight of B, D, Eis 42 kg and the weight of Fis equal to that of B. What is the average weight of A, B, C, D, Eand F?
A cow costs more than 4 goats but less than 5 goats. If a goat costs between Rs. 600 and Rs. 800, which of the following is a most valid conclusion?
