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Question
Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by
the Meteorological Department are given below: 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9
(i) Find the mean 𝑋 ̅
(ii) Verify that = `sum _ ( i = 1)^10`(xi - x ) = 0
Solution
Duration of sunshine (in hours) for 10 days are
= 9.6, 5.2, 3.5,1.5,1.6, 2.4, 2.6,8.4,10.3,10.9
(i) Mean x = `"Sum of all numbers "/"Total numbers"`
= `(9.6 + 5.2 + 3.5 +1.5 +1.6 + 2.4 + 2.6 + 8.4 +10.3 +10.9)/ 10`
` = 56 / 10 = 5.6`
(ii) LHS = `sum _(i = 1)^10`
= ( x1 - x ) + ( x2 - x ) + ( x3 - x ) + .............. + ( x10 - x )
= (9.6 - 5.6) + (5.2 - 5.6) + (3.5 - 5.6) + (1.5 - 5.6) + (1.6 - 5.6) + (2.4 - 5. 6)
= (4) + (-0.4) + (-2.1) - 4 .1- 4 - 3.2 - 3 + 2.8 + 4.7 + 5.3
= 16.8 - 16.8
= 0
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