**Range**

$$ Range = L - S $$

where L= largest item; S = smallest item.

The relative measure corresponding to range, called the coefficient of range is obtained by applying the following formula:

$$ Coefficient \,of \,Range \,= \,{{\frac{L - S }{L + S}}} $$

**Individual Series**

Table 6.2 | |
---|---|

Year | Profit (in 000 Rs) |

1985 | 40 |

1986 | 30 |

1987 | 80 |

1988 | 100 |

1989 | 115 |

1990 | 85 |

1991 | 210 |

1992 | 230 |

Here L = 230; S = 30.

Range = 230 - 30 = 200

$$ Coefficient \,of \,Range \,= \,{{\frac{L - S }{L + S}}} $$ $$ = \,{{\frac{230 - 30 }{230 + 30}}} $$ $$ = \,{{\frac{200 }{260}}} $$ $$ = \,{{0.77}} $$

**Discrete Series**

Table 6.3 | |
---|---|

Size | Frequency |

5 | 7 |

10 | 8 |

15 | 12 |

20 | 16 |

25 | 21 |

30 | 17 |

35 | 12 |

40 | 4 |

$$ Range = L - S $$

Here L = 40; S = 5.

Range = 40 - 5 = 35

$$ Coefficient \,of \,Range \,= \,{{\frac{L - S }{L + S}}} $$ $$ = \,{{\frac{40 - 5 }{40 + 5}}} $$ $$ = \,{{\frac{35}{45}}} $$ $$ = \,{{0.78}} $$

**Continuous Series**

For continuous series, range is calculated either by subtracting the lower limit of the lowest class from the upper limit of the highest class or by subtracting the mid-value of the lowest class from the midvalue of the highest class.

Table 6.4 | |
---|---|

Daily Wage | Number of Workers |

80 - 100 | 12 |

100 - 120 | 18 |

120 - 140 | 24 |

140 - 160 | 27 |

160 - 180 | 32 |

180 - 200 | 20 |

Here L = 200; S = 80.

Range = 200 - 80 = 120

$$ Coefficient \,of \,Range \,= \,{{\frac{L - S }{L + S}}} $$ $$ = \,{{\frac{200 - 80 }{200 + 80}}} $$ $$ = \,{{\frac{120}{280}}} $$ $$ = \,{{0.43}} $$

Table 6.5 | |
---|---|

Class midpoints | Frequency |

2 | 3 |

5 | 5 |

8 | 6 |

11 | 8 |

14 | 6 |

17 | 4 |

20 | 1 |

Here L = 20; S = 2.

Range = 20 - 2 = 18

$$ Coefficient \,of \,Range \,= \,{{\frac{L - S }{L + S}}} $$ $$ = \,{{\frac{20 - 2 }{20 + 2}}} $$ $$ = \,{{\frac{18}{22}}} $$ $$ = \,{{0.82}} $$

**MERITS OF RANGE**

- Easy to compute.
- It gives the maximum spread of data.
- Easy to understand.

**DEMERITS OF RANGE**

- It is affected greatly by sampling fluctuations.
- It is not based on all the observations.
- It cannot be used in case of open-end distribution.