Marks Number of Students 20 - 30 5 30 - 40 12 40 - 50 10 50 - 60 15 60 - 70 8
Calculating Mean Marks from Grouped Data
To find the mean marks obtained by the students, we need to calculate the mean of the grouped frequency distribution.
Steps for Mean Calculation
- Determine the midpoint (\(x_i\)) for each marks interval. The midpoint is calculated as \(\frac{\text{Lower Limit} + \text{Upper Limit}}{2}\).
- Multiply each midpoint (\(x_i\)) by the corresponding number of students (frequency, \(f_i\)) to get the product \(f_i x_i\).
- Sum all the products (\(f_i x_i\)).
- Sum all the frequencies (\(f_i\)). This is the total number of students (\(N\)).
- Calculate the mean using the formula: Mean = \(\frac{\sum (f_i x_i)}{N}\).
Data and Calculation Table
| Marks Interval | Number of Students (\(f_i\)) | Midpoint (\(x_i\)) | \(f_i x_i\) |
| 20 - 30 | 5 | \(\frac{20+30}{2} = 25\) | \(5 \times 25 = 125\) |
| 30 - 40 | 12 | \(\frac{30+40}{2} = 35\) | \(12 \times 35 = 420\) |
| 40 - 50 | 10 | \(\frac{40+50}{2} = 45\) | \(10 \times 45 = 450\) |
| 50 - 60 | 15 | \(\frac{50+60}{2} = 55\) | \(15 \times 55 = 825\) |
| 60 - 70 | 8 | \(\frac{60+70}{2} = 65\) | \(8 \times 65 = 520\) |
| Total | \(N = 50\) | \(\sum f_i x_i = 2340\) |
Final Mean Calculation
Using the sums calculated:
Mean = \(\frac{\sum f_i x_i}{N} = \frac{2340}{50}\)
Mean = \(46.8\)
The mean marks obtained by students is 46.8.
Similar Questions
- What is the mode of the following data?
44, 45, 51, 50, 53, 54, 46, 40, 51, 46, 40, 42, 55, 42, 44, 55, 49, 44 - The marks obtained by 9 students of a class in mathematics are 76, 85, 47, 67, 85, 76, 47, 76, 67. What is the mode of these numbers?
- What is the mode of the following data?
89, 76, 76, 88, 81, 81, 65, 90, 83, 89, 64, 63, 78, 64, 82, 87, 79, 89, 87, 65, 86, 77, 80, 70, 67 - What is the mode of the following data?
86, 84, 71, 82, 82, 63, 84, 71, 70, 86, 88, 65, 71, 81, 87, 60, 60, 74, 78, 62, 75, 66, 68, 85, 72 - What is the mode of the following data?
89, 89, 64, 86, 64, 79, 81, 85, 82, 81, 75, 85, 82, 84, 61, 82, 81, 64, 74, 71, 61, 68, 77, 64, 79 - What is the mode of the following data?
55, 50, 48, 43, 55, 41, 54, 51, 41, 45, 53, 54, 52, 41, 49, 54, 41, 49 - What is the mode of the following data?
70, 70, 73, 71, 74, 69, 80, 68, 66, 66, 89, 83, 81, 86, 82, 74, 86, 87, 67, 72, 62, 76, 86, 65, 62 - What is the mode of the following data?
78, 60, 85, 76, 84, 86, 73, 89, 78, 77, 60, 63, 62, 72, 61, 78, 67, 77, 61, 78, 75, 61, 88, 66, 69 - What is the mode of the following data?
70, 79, 66, 89, 68, 80, 82, 80, 71, 84, 69, 68, 61, 85, 71, 84, 68, 86, 73, 75, 83, 88, 64, 88, 65 - What is the mode of the following data?
48, 42, 46, 42, 44, 43, 48, 49, 48, 45, 53, 46, 47, 47, 49, 53, 50, 41
Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2What is the mode of the given data?
21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
