Vocational training copleents traditional education by providing … - Vidyadip

Question

Vocational training copleents 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 eployability thus aking the student self-reliant. Keeping this in view, a teacher ade the following table grving the frequency distribution of students/adults undergoing vocational training fro the training institute.
Iage

Iage

Age (in years)	15-19	20-24	25-29	30-34	35-39	40-44	45-49	50-54
Nuber of participants	62	132	96	37	13	11	10	4

Fro the above, answer the following questions:
(i) What is the lower liit of the odal class of the above data?
(ii) (a) Find the edian class of the above data.
OR
(b) Find the nuber of participants of age less than 50 years who undergo vocational training.
(iii) Give the epirical relationship between ean, edian and ode.

✓

Answer

(i) Converting the frequency distribution into inclusive form, we obtain the following frequency distribution

Clearly, class 19.5-24.5 has the maximum frequency 132. So, 19.5-24.5 is the modal class.
(ii) (a) The cumulative frequency distribution is as given below:

Age (in years)	Number of participants	Cumulative frequency
14.5-19.5	62	62
19.5-24.5	132	194
24.5-29.5	96	290
29.5-34.5	37	327
34.5-39.5	13	340
39.5-44.5	11	351
44.5-49.5	10	361
49.5-54.5	4	365
		$N=\Sigma f_i=365$

We have, N= 365 $\Rightarrow \frac{ N }{2}=182.5$
The cumulative frequency just greater than $\frac{N}{2}$ =182.5 is 194 and the corresponding class is 19.5-24.5. So, 19.5-24.5 is the median class.
OR
(ii) (b) Clearly, number of participants of age less than 50 years is the cumulative frequency corresponding to the class 44.5-49.5 and is equal to 361. Thus, there are 361 participants of age less than 50 years.
(iii) The empirical ralation between mean, median and mode is:
Mode 3 Median -2 Mean.

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