The mode of the following distribution is 65.625 hours. Find the value of p.
Lifetime (in hours) 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 10 35 52 60 p 29
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Given :
Lifetime (in hours) 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 10 35 52 60 p 29
Mode 65.625
To Find : value of p
Solution:
Mode is 65.625 lies between 60-80
Lifetime (in hours) f
0-20 10
20-40 35
40-60 52
60-80 60
80-100 p
100-120 29
Mode = 60 + 20 * ( 60 - 52)/ (60 - 52 + 60 - p)
=> 65.625 = 60 + 20 * ( 8)/ ( 68 - p)
=> 5.625 = 160 / ( 68 - p)
=> p = 39.56
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