CALCULATE STANDARD DEVIATION AND COEFFICENT OF VARIATION

Question

X	10-20	20-30	30-40	40-50	50-60
F	7	3	6	10	15

Question: For the above continuous data; calculate the standard deviation and the coefficient of variation

Answer 1

For X we take the central datum as representative of the range, so, for example, 10-20 would be represented by 15. The sum of the data is 7×15+3×25+6×35+10×45+15×55=5(21+15+42+90+165)=1665.

The number of observations=7+3+6+10+15=41, so the mean, μ, is 1665/41=40.61 approx.

To calculate the standard deviation, we first need the variance, σ²:

{7(15-μ)²+3(25-μ)²+6(35-μ)²+10(45-μ)²+15(55-μ)²}/41=214.8721, standard deviation, σ=14.66 approx.

Coefficient of variation=σ/μ=0.36 approx.