From the data given below . calculate the mean wage, correct to the nnearst rupee.

category |
A |
B |
C |
D |
E |
F |

Wages (Rs,day)(x) |
50 | 60 | 70 | 80 | 90 | 100 |

no.of workers |
2 | 4 | 8 | 12 | 10 | 6 |

(1) If the number of workers in each category is doubled, , what would be the new mean wage?

(2) If the wages per day in each category are incresed by 60% what is the new mean wages?

(3) If the number of workers in each caategory is doubled is and the wages per day worker are reduced by 40%, what would be the new mean wage?

#### Solution

Wages (Rs/day) (x) | No.of Workers (f) | fx |

50 | 2 | 100 |

60 | 4 | 240 |

70 | 8 | 560 |

80 | 12 | 960 |

90 | 10 | 900 |

100 | 6 | 600 |

Total | 42 | 3360 |

`barx=(Σ fx)/(∑ f) =3360/42=80`

(1) Mean remains the same if the number of workers in each category is doubled

Mean =80

(2) Mean will be inceased by 60% if the wages per day worker is increased by 60%

New mean =`80xx160/100=128`

(3) No change in the mean if the number of workers is doubled but if wages per workes is reduced by 40%, then

New mean=`80xx60/100=48`