To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below: Concentration of SO2 (in ppm) Frequency 0.00–0.04 4 0.04–0.08 9 0.08–0.12 9 0.12–0.16 2 0.16–0.20 4 0.20–0.24 2 Find the mean concentration of SO2 in the air.

Concentration of SO2(In ppm) Mid-value(xi) Frequency(fi) fixi
0.00–0.04 0.02 4 0.08
0.04–0.08 0.06 9 0.54
0.08–0.12 0.10 9 0.90
0.12–0.16 0.14 2 0.28
0.16–0.20 0.18 4 0.72
0.20–0.24 0.22 2 0.44
Total 30 2.96
Let x̄ be the required mean.
Mean, x̄ = (1/n) Σfixi
Here, n=30, Σfixi=2.96
Therefore, Mean, x̄ = 2.96/30 = 0.099 ppm
We have used the direct method because numerical values of f and x are small.