Marks Number of Candidates More than 10 100 More than 20 75 More than 30 60 More than 40 40
To find the average marks of the candidates, we have to convert this cumulative frequency distribution into a frequency distribution, and then determine the mean.
- First, create intervals and frequencies:
- Marks > 10 implies 10-20 candidates: \(100 - 75 = 25\)
- Marks > 20 implies 20-30 candidates: \(75 - 60 = 15\)
- Marks > 30 implies 30-40 candidates: \(60 - 40 = 20\)
- Marks > 40 implies 40-50 candidates: \(40 - 0 = 40\)
- Summarize this as a frequency table:
| Marks Interval | Number of Candidates (f) |
|---|---|
| 10-20 | 25 |
| 20-30 | 15 |
| 30-40 | 20 |
| 40-50 | 40 |
- Find the midpoint (x) for each interval:
- 10-20: \(x = \frac{10 + 20}{2} = 15\)
- 20-30: \(x = \frac{20 + 30}{2} = 25\)
- 30-40: \(x = \frac{30 + 40}{2} = 35\)
- 40-50: \(x = \frac{40 + 50}{2} = 45\)
- Calculate the sum of the products of midpoints and frequencies: \(\sum (f \cdot x) = 25 \times 15 + 15 \times 25 + 20 \times 35 + 40 \times 45\)
- \(= 375 + 375 + 700 + 1800\)
- \(= 3250\)
- Find the sum of frequencies: \(\sum f = 25 + 15 + 20 + 40 = 100\)
- Calculate mean (average) using the formula: \(\text{Mean} = \frac{\sum (f \cdot x)}{\sum f} = \frac{3250}{100} = 32.5\)
Therefore, the average marks of the candidates are 32.5.
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.
