#### Question

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`

#### Related QuestionsVIEW ALL [72]

Draw an ogive for the data given beelow and from the graph determine:

(1) the median marks

(2) the number of students who obtained more than 75% marks

Marks |
No.of students |

0-9 | 5 |

10-19 | 9 |

20-29 | 16 |

30-39 | 22 |

40-49 | 26 |

50-59 | 18 |

60-69 | 11 |

70-79 | 6 |

80-89 | 4 |

90-99 | 3 |

Find the mode and median of the following frequency distribution

x | 10 | 11 | 12 | 13 | 14 | 15 |

f | 1 | 4 | 7 | 5 | 9 | 3 |

The mean of the following distribution in 52 and the frequency of class interval 30-40 'f' find f

C.I |
10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

freq |
5 | 3 | f | 7 | 2 | 6 | 13 |

Calculate the mean of the following distribution using step deviation method.

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Number of students |
10 | 9 | 25 | 0 | 16 | 10 |

By drawing an ogive, estimate the following frequency distribution:

Weight (kg) | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |

No.of boys | 11 | 25 | 12 | 5 | 2 |