Question
Download Solution PDFThe score in Maths of 50 students of a class is given in the following table. Calculate the mean score.
| Interval | Frequencies |
| 0-10 | 2 |
| 10-20 | 11 |
| 20-30 | 28 |
| 30-40 | 6 |
| 40-50 | 3 |
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total number of students = 50
| Interval | Frequencies |
| 0-10 | 2 |
| 10-20 | 11 |
| 20-30 | 28 |
| 30-40 | 6 |
| 40-50 | 3 |
Concept Used:
Mean = Total Sum of f(x) ÷ Total Sum of f
Calculation:
⇒ Firstly for each interval, we will find the midpoint of it.
⇒ For interval 0-10, Midpoint = \(\frac{0+10}{2}\) = 5
⇒ For interval 10-20, Midpoint = \(\frac{10+20}{2}\) = 15
| Interval | Frequencies (f) | Midpoint (x) |
| 0-10 | 2 | 5 |
| 10-20 | 11 | 15 |
| 20-30 | 28 | 25 |
| 30-40 | 6 | 35 |
| 40-50 | 3 | 45 |
| Total | 50 | 125 |
⇒ Now, to calculate the values of f(x), multiply each midpoint with their respective frequencies.
| Interval | Frequencies (f) | Midpoint (x) | f(x) |
| 0-10 | 2 | 5 | 10 |
| 10-20 | 11 | 15 | 165 |
| 20-30 | 28 | 25 | 700 |
| 30-40 | 6 | 35 | 210 |
| 40-50 | 3 | 45 | 135 |
| Total | 50 | 125 | 1220 |
⇒ So, Mean = \(\frac{\sum f(x)}{\sum f}\)
⇒ Mean = \(\frac{1220}{50}\) =24.4
Hence, the mean score of the students is 24.4.
Last updated on May 28, 2025
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