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# The following table gives the distribution of the lifetime of 400 neon lamps:

Life time: (in hours) | Number of lamps |

1500-2000 | 14 |

2000-2500 | 56 |

2500-3000 | 60 |

3000-3500 | 86 |

3500-4000 | 74 |

4000-4500 | 62 |

4500-5000 | 48 |

Find the median lifetime of a lamp."

Given:

The given table gives the distribution of the lifetime of 400 neon lamps.

To do:

We have to find the median life.

Solution:

Here,

$N = 400$

$\frac{N}{2} = \frac{400}{2} = 200$

The cumulative frequency just greater than $\frac{N}{2}$ is 216 and the corresponding class is 3000 – 3500.

This implies, that 3000– 3500 is the median class.

Therefore,

$l = 3000, f = 86, F = 130$ and $h = (3500 - 3000) = 500$

Median $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$

$=3000+\frac{200-130}{86} \times 500$

$=3000+\frac{70}{86} \times 500$

$=3000+\frac{35000}{86}$

$= 3000 + 406.98$

$= 3406.98$

The median life is 3406.98 hours.

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