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
Find the median of the data 11, 16, 33, 15, 51, 19, 71, 75, 21, 17.
For a data, if the mean is 28.5 and the median is 32, then the mode using empirical formula is:
- If the mean of a distribution is 8.73 and its median is 11, then the mode of the distribution is __________ (using empirical relation).
- If the median and mode of a data of 20 numbers are 250 and 295, respectively, then find the sum of the 20 numbers.
- 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 - The median of \(\frac{3}{7}\), \(\frac{3}{5}\), \(\frac{11}{13}\), \(\frac{14}{16}\) and \(\frac{17}{19}\) is _____.
- 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 - The lifetime of certain species is given in the following table. Calculate the modal lifetime (rounded up to one decimal place) in days.
Lifetime (days) 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 10 35 52 61 38 29 - Find the mean of the mode and the median of the given data.
15, 3, 8, 7, 6, 5, 5, 7, 18, 7
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
