Coefficient of Variation worksheet

1. Coefficient of variation: 46.78%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{3+4+3+3+5+4+6+10}{8}$$=4.75$

2. Find the population standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n, then take the square root

   $\sigma$$=\sqrt{\frac{39.5}{8}}$$=2.222049$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2.222049}{4.75}\times 100$$=\mathrm{46.779971\%}$

2. Coefficient of variation: 40%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+4+4+4+5+5+7+9}{8}$$=5$

2. Find the population standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n, then take the square root

   $\sigma$$=\sqrt{\frac{32}{8}}$$=2$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2}{5}\times 100$$=\mathrm{40\%}$

3. Coefficient of variation: 42.76%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+4+4+4+5+5+7+9}{8}$$=5$

2. Find the sample standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n − 1, then take the square root

   $s$$=\sqrt{\frac{32}{7}}$$=2.13809$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2.13809}{5}\times 100$$=\mathrm{42.761799\%}$

4. Coefficient of variation: 51.12%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+3+4+4+7+6+9+10}{8}$$=5.625$

2. Find the sample standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n − 1, then take the square root

   $s$$=\sqrt{\frac{57.875}{7}}$$=2.875388$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2.875388}{5.625}\times 100$$=\mathrm{51.118012\%}$

5. Coefficient of variation: 44.17%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+4+4+3+4+3+7+8}{8}$$=4.375$

2. Find the population standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n, then take the square root

   $\sigma$$=\sqrt{\frac{29.875}{8}}$$=1.932453$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{1.932453}{4.375}\times 100$$=\mathrm{44.170357\%}$

6. Coefficient of variation: 44.66%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+4+4+3+6+5+5+9}{8}$$=4.75$

2. Find the sample standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n − 1, then take the square root

   $s$$=\sqrt{\frac{31.5}{7}}$$=2.12132$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2.12132}{4.75}\times 100$$=\mathrm{44.659376\%}$

7. Coefficient of variation: 39.4%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+4+4+3+4+5+7+7}{8}$$=4.5$

2. Find the sample standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n − 1, then take the square root

   $s$$=\sqrt{\frac{22}{7}}$$=1.772811$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{1.772811}{4.5}\times 100$$=\mathrm{39.395789\%}$

8. Coefficient of variation: 40.19%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+3+4+5+5+5+8+7}{8}$$=4.875$

2. Find the sample standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n − 1, then take the square root

   $s$$=\sqrt{\frac{26.875}{7}}$$=1.95941$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{1.95941}{4.875}\times 100$$=\mathrm{40.193016\%}$

9. Coefficient of variation: 45.36%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{1+4+5+5+5+4+8+8}{8}$$=5$

2. Find the sample standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n − 1, then take the square root

   $s$$=\sqrt{\frac{36}{7}}$$=2.267787$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2.267787}{5}\times 100$$=\mathrm{45.355737\%}$

10. Coefficient of variation: 46.41%

1. Find the mean (average) of the 8 values, the yardstick the spread is measured against

   $\mathrm{x̄}$$=\frac{2+4+5+4+5+5+6+11}{8}$$=5.25$

2. Find the population standard deviation, the typical distance of a value from the mean. Square each distance, add them, divide by n, then take the square root

   $\sigma$$=\sqrt{\frac{47.5}{8}}$$=2.436699$

3. Divide the standard deviation by the mean, so the spread is measured relative to the size of the values, and multiply by 100 for a percentage

   $\mathrm{CV}$$=\frac{2.436699}{5.25}\times 100$$=\mathrm{46.413306\%}$