To find out concentration of \(SO_2\) 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. Find the mean concentration of \(SO_2\) in the air.

Maths Questions, Statistics Questions / By

Question :

Concentration of \(SO_2\) (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

Solution :

Let the assumed mean a = 0.10

Concentration of \(SO_2\) (in ppm) Frequency (\(f_i\)) Mid – Value (\(x_i\)) \(u_i\) = \(x_i – 0.10\over 0.04\) \(f_iu_i\)
0.00 – 0.04 4 0.02 -2 -8
0.04 – 0.08 9 0.06 -1 -9
0.08 – 0.12 9 0.10 0 0
0.12 – 0.16 2 0.14 1 2
0.16 – 0.20 4 0.18 2 8
0.20 – 0.24 2 0.22 3 6
\(\sum f_i\) = 30 \(\sum f_iu_i\) = -1

By step deviation method :

Mean = a + \(\sum f_iu_i\over \sum f_i\) \(\times\) h = 0.10 + \(-1\over 30\) \(\times\) 0.04

= 0.10 – 0.0013 = 0.0987

= 0.099 ppm

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