The following table shows the distribution of weights of $100$ candidates appearing for a competition. Determine the model weight.
Weight $(i n k g)$ $50 - 55$ $55 - 60$ $60 - 65$ $65 - 70$ $70 - 75$ $75 - 80$
Number of candidates $13$ $18$ $45$ $16$ $06$ $02$

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Solution

Weight No. of candidates
50-55 13
55-60 10
60-65 45
65-70 16
70-75 06
75-80 02
The model weight is $60 - 65$
We know,
$m o d e = l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h$
$f = 45$ $f_{2} = 16$
$f_{1} = 10$ $h = 5$
$l = 60$
$= 60 + \frac{45 - 10}{2 \times 45 - 16 - 10} \times 5$
$= 60 + \frac{27}{56} \times 5$
$= 60 + \frac{135}{56}$
$= 60 + 2.4$
$= 62.4$

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Weight $(i n k g)$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Number of candidates	$13$	$18$	$45$	$16$	$06$	$02$

Weight	No. of candidates
50-55	13
55-60	10
60-65	45
65-70	16
70-75	06
75-80	02

The following table shows the distribution of weights of 100 candidates appearing for a competition. Determine the model weight.Weight (in kg)50−5555−6060−6565−7070−7575−80Number of candidates 131845160602

Weight No. of candidates 50-5513 55-60 10 60-65 45 65-70 16 70-75 06 75-80 02 The model weight is 60−65 We know,mode=l+f−f12f−f1−f2×hf=45 f2=16f1=10 h=5l=60=60+45−102×45−16−10×5=60+2756×5=60+13556=60+2.4=62.4

The following table shows the distribution of weights of $100$ candidates appearing for a competition. Determine the model weight.
Weight $(i n k g)$ $50 - 55$ $55 - 60$ $60 - 65$ $65 - 70$ $70 - 75$ $75 - 80$
Number of candidates $13$ $18$ $45$ $16$ $06$ $02$