Q1. [4]
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:
$$\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$$
---
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.
If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to
Library and find the actual CBSE question paper. The original papers are also available on the CBSE website:
cbse.gov.in.