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`(x_i - x ) = 0 

Answer 1

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