Vocational training complements traditional education . . .

Question : 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.

Age (in years)	15-19	20-24	25-29	30-34	35-39	40-44	45-49	50-54
No. of participants	62	132	96	37	13	11	10	4

From the above answer the following questions :

(i) What is the lower limit of the modal class of the above data? [1 Mark]

(ii) (a) Find the median class of the above data. [2 Marks]

(b) Find the number of participants of age less than 50 years who undergo vocational training.

(iii) Give the empirical relationship between the mean, median and mode. [1 Mark]

CBSE 2024 (30/3/1)

Solution :

This is a case study based question form Class 10th Statistics.

Here the class intervals are not continuous so first of all we have to make them continuous.

As we can see that here the gap is 1 (15-19, 20-24)

So we will subtract 0.5 (1/2=0.5) from the lower limit and add 0.5 to the upper limit.

Modified continuous frequency distribution table is given below

Age (in years)	14.5-19.5	19.5-24.5	24.5-29.5	29.5-34.5	34.5-40.5	39.5-44.5	44.5-49.5	49.5-54.5
No. of participants	62	132	96	37	13	11	10	4

i) Maximum frequency = 132
Modal Class = 19.5-24.5
Lower Limit of the modal class = 19.5

ii)

Age (in years)	14.5-19.5	19.5-24.5	24.5-29.5	29.5-34.5	34.5-40.5	39.5-44.5	44.5-49.5	49.5-54.5
No. of participants	62	132	96	37	13	11	10	4
Cumulative Frequency (CF)	62	194	290	327	340	351	361	365

(a) Total number of observations (N) = 365
N/2 = 365/2 = 182.5

Hence, the required Median Class is 19.5-24.5

OR

(b) Number of participants of age less than 50 years = 365-4 = 361

(iii) 3Media = 2Mean+Mode
which is the required empirical relation between mean, median and mode.

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Vocational training complements traditional education . . .