We may calculate class marks (xi) for each interval by using the relation
xi \(=\frac{Upper\,class\,limit+lower\,class\,limit}{2}\)
Class size = 0.04
Now taking 0.14 as assumed mean (A), we can calculate as follows:
Concentration So2 (ppm) |
Frequencey (fi) |
xi |
di = xi - 0.14 |
ui |
fiui |
0.00 - 0.04 |
4 |
0.02 |
-0.12 |
-3 |
-12 |
0.04 - 0.08 |
9 |
0.06 |
-0.08 |
-2 |
-18 |
0.08 - 0.12 |
9 |
0.10 |
-0.04 |
-1 |
-9 |
0.12 - 0.16 |
2 |
0.14 |
0 |
0 |
0 |
0.16 - 0.20 |
4 |
0.18 |
0.04 |
1 |
4 |
0.20 - 0.24 |
2 |
0.22 |
0.08. |
2 |
4 |
|
N = 30 |
|
|
|
\(\sum\)fiui = -31 |
Mean (x̅) = A + \(\frac{\sum f_iu_i}{N}\times h\)
\(=0.14+\frac{-31}{30}\times(0.04)\)
\(=0.14-0.04133\)
\(=0.099\)ppm
SO,
mean concentration of SO2 in the air is 0.099 ppm