Sum

The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.

Average Speed of
Vehicles(Km/hr) |
60 - 64 | 64 - 69 | 70 - 74 | 75 - 79 | 79 - 84 | 84 - 89 |

No. of vehicles | 10 | 34 | 55 | 85 | 10 | 6 |

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#### Solution

Class(Number of working hours) |
Continuousclasses |
Frequency(Number of workers) |
Cumulaive frequency less than theupper limit |

60 - 64 | 59.5 - 64.5 | 10 | 10 |

64 - 69 | 64.5 - 69.5 | 34 | 44 |

70 - 74 | 69.5 - 74.5 | 55 | 99 → cf |

75 - 79 | 74.5 - 79.5 | 85 → f | 184 |

79 - 84 | 79.5 - 84.5 | 10 | 194 |

84 - 89 | 84.5 - 89.5 | 6 | 200 |

Total | - | N = 200 | - |

Here, total frequency = ∑fi = N = 200

∴ `"N"/2 = 200/2 = 100`

Cumulative frequency which is just greater than (or equal) to 100 is 184.

∴ The median class is 74.5 – 79.5.

Now, L = 74.5, f = 85, cf = 99, h = 5

Now, Median = \[L + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h\]\

`= 74.5 + ((100 - 99)/85) xx 5`

= 74.5 + 0.059

= 74.559 ≈ 75

∴ The median of the given data is 75 km/hr (approx.).

Concept: Tabulation of Data

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