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# 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 |

No. of components: | 10 | 35 | 52 | 61 | 38 | 29 |

Determine the modal lifetimes of the components."

Given:

The given data gives information on the observed lifetimes (in hours) of 225 electrical components.

To do:

We have to determine the modal lifetimes of the components.

Solution:

The frequency of the given data is as given below.

Lifetimes (in hours) ($x_i$): | No. of components $(f_i$): |

0-20 | 10 |

20-40 | 35 |

40-60 | 52 |

60-80 | 61 |

80-100 | 38 |

100-120 | 29 |

We observe that the class interval of 60-80 has the maximum frequency(61).

Therefore, it is the modal class.

Here,

$l=60, h=20, f=61, f_1=52, f_2=38$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=60+\frac{61-52}{2 \times 61-52-38} \times 20$

$=60+\frac{9}{122-90} \times 20$

$=60+\frac{180}{32}$

$=60+5.625$

$=65.625$

The modal lifetimes of the components are 65.625 years.

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