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The weekly observations on cost of living index in a certain city for the year 2004-2005 are given below. Compute the weekly cost of living index.

 Cost of living cost of living  Number of students  Cost of living index  Number of students
 1400 - 1500 3  1700 - 1800  9
 1500 - 1600 10  1800 - 1900  6
 1600 - 1700 20  1900 - 2000 2

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Best answer

Let the assumed mean (A) = 1650

 Class interval  Mid value (xi)  di = xi - A = xi - 1650  ui\(\frac{xi-1650}{100}\)  Frequency (fi)  fiui
 1400 - 1500  1450 -200 -2 3 -10
 1500 - 1600 1550 -100 -1 10 -10
 1600 - 1700 1650 0 0 20 0
 1700 - 1800  1750 100 1 9 9
 1800 - 1900 1850 200 2 6 12
 1900 - 2000 1950 300 3 2 6
 N = 52 \(\sum\)fiui =.7

We have, 

A = 1650

h = 100

Mean = A + h \(\times\frac{\sum f_iu_i}{N}\)

\(=1650+100\times\frac{7}{52}\)

\(=1650 + \frac{1650}{13}\)

\(=\frac{21450+175}{13}=\frac{21625}{13}\)

\(=1663.46\)

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