Following data represents life period observations of electrical instruments.
Life period (in hrs) 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 100 35 52 61 38 29
Find mode of life period of instruments.

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Solution

Here maximum frequency is 61 and its corresponding class-interval is 60 - 80. So modal class = 60 - 80.
$l = 60, f_{1} = 61, f_{0} = 52, f_{2} = 38,$ and $h = 20$
$M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h = 60 + (\frac{61 - 52}{2 \times 61 - 52 - 38}) \times 20$
$= 60 + \frac{9}{122 - 52 - 38} \times 20 = 60 + \frac{9}{32} \times 20$
$60 + \frac{180}{32} = 60 + 5.625 = 65.625$
Thus, mode of life period is 65.625 hrs.

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Life period (in hrs)	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	100	35	52	61	38	29