Class 10

Math

All topics

Statistics

The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:

Lifetimes (in hours) | $0−20$ | $20−40$ | $40−60$ | $60−80$ | $80−100$ | $100−120$ |

Frequency | $10$ | $35$ | $52$ | $61$ | $38$ | $29$ |

So, it is the modal class

Now, $l=$ Lower limit of modal class $=60$

$f_{1}=$ Frequency of modal class $=61$

$f_{0}=$ Frequency of class preceding the modal class $=52$

$f_{2} =$ Frequency of class succeeding the modal class $=38$

$h=$ Class interval width = 20

So, Mode $=l+(2f_{1}−f_{0}−f_{2}f_{1}−f_{0} )×h$

$=60+(2(61)−52−3861−52 )×20$

$=60+(122−909 )×20$

$=60+(329 )×20$

$=60+5.625$

Mode $=65.625$

Therefore, modal lifetime of electrical components is $65.625$ hours

Therefore, modal lifetime of electrical components is $65.625$ hours