Q1. [4] § 13.4 Median of Grouped Data
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self-reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
From the above answer the following questions :
- (i) What is the lower limit of the modal class of the above data ? [1]
- (ii) Find the median class of the above data. [2]
- (iii) Give the empirical relationship between mean, median and mode. [1]
Previously asked in CBSE board exam
2024 30/3/1 Q37
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding stimulus
Model Answer
Given data:
| Age (years) | Frequency | Cumulative Frequency |
|-------------|-----------|----------------------|
| 15–19 | 62 | 62 |
| 20–24 | 132 | 194 |
| 25–29 | 96 | 290 |
| 30–34 | 37 | 327 |
| 35–39 | 13 | 340 |
| 40–44 | 11 | 351 |
| 45–49 | 10 | 361 |
| 50–54 | 4 | 365 |
Total N = 365
(i) The highest frequency is 132, corresponding to class 20–24.
∴ Lower limit of modal class = 20
(ii) N/2 = 365/2 = 182.5
The cumulative frequency just greater than 182.5 is 194 (class 20–24).
∴ Median class = 20–24
(iii) Empirical relationship:
$$\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$$
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Explanation
- Modal class is the class with the highest frequency (132); its lower limit is simply the starting value of that class.
- Median class is found by locating N/2 = 182.5 in the cumulative frequency column — the class whose cumulative frequency first exceeds this value.
- The empirical formula (Mode = 3 Median − 2 Mean) is a standard result from the Statistics chapter; students must reproduce it exactly as given in the NCERT textbook.
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