# Coefficient of Variation

If there are two or more sets of distributions, in order to decide which of the two distributions has more variability, we compare their coefficients of variation(C.V.).

C. V = . The distribution with greater C.V is said to be more variable. A set of readings with less variability is said to be more stable or consistent

Group | Mean | S.D |

I | ||

II |

. Compare these values. If two sets of readings have the same mean and different standard deviations, then the reading with smaller S.D is said to be more consistent or less variable.

**Example 1:**

The marks of two students A and B is 12 tests are given below Identity the better student and the more consistent student.

A |
75 |
74 |
78 |
72 |
78 |
77 |
79 |
81 |
79 |
76 |
72 |
71 |

B |
87 |
84 |
80 |
88 |
89 |
85 |
86 |
82 |
82 |
79 |
86 |
80 |

**Solution:**

Let

*x*denote the marks of A and the assumed mean for

*x*be 76.

Let

*y*denote the marks of B and the assumed mean for

*y*be 76.

N = 12.

75 74 78 72 78 77 79 81 79 76 72 71 |
âˆ’ 1 âˆ’ 2 2 âˆ’ 4 2 1 3 5 3 0 âˆ’ 4 âˆ’ 5 |
1 4 4 16 4 1 9 25 9 0 16 25 |
87 84 80 88 89 85 86 82 82 79 86 80 |
3 0 âˆ’ 4 4 5 1 2 âˆ’ 2 âˆ’ 2 âˆ’ 5 2 âˆ’ 4 |
9 0 16 16 25 1 4 4 4 25 4 16 |

912 |
0 |
114 |
1008 |
0 |
124 |

[Here assumed mean = actual mean. Hence Î£ d = 0]

(Assumed mean = actual mean)

C.V. of A == 3.215

C.V. of B =

**Conclusion:**

B's average score is more than that of A. B is a better student.

C.V of B is smaller than that of A. B is a more consistent preformer than A.

**Example 2:**The runs scored by two batsmen in ten innings are as follows:

A |
10 |
115 |
5 |
73 |
7 |
120 |
36 |
84 |
29 |
19 |

B |
45 |
12 |
76 |
42 |
4 |
50 |
37 |
48 |
13 |
0 |

**Solution:**Let be scores of A; Assumed mean = 50

be scores of B; Assumed mean = 50

10
115 5 73 7 120 36 84 29 19 |
âˆ’ 40
65 âˆ’ 45 23 âˆ’ 43 70 âˆ’ 14 34 âˆ’ 21 âˆ’ 31 |
1600
4225 2025 529 1849 4900 196 1156 441 961 |
45
12 76 42 4 50 37 48 13 0 |
âˆ’ 5
âˆ’ 38 26 âˆ’ 8 âˆ’ 46 0 âˆ’ 13 âˆ’ 2 âˆ’ 37 âˆ’ 50 |
25
1444 676 64 2116 0 169 4 1369 2500 |

498 | âˆ’ 2 | 17882 | 327 | âˆ’ 173 | 8367 |

** **

A is a better player.

C.V of B < C.V of A

B is more consistent than A.

**Note:**

- Adding (or subtracting) the same positive number to each observation in a group does not affect the variance and hence S.D.
- If each observation is multiplied by a non - zero constant 'K' the variance of the resulting observations becomes K
^{2}times the original variance. The new S.D become K times the original S.D.