the table below gives the distribution of village under different height from sea level in certain reign compute the mean height of the region by short-cut method. height(in meters): 200 600 1000 1400 1800 2200 number village: 142 265 560 271 89 16

Answer 1

A = Assumed mean in this case A = 1400

x = height

N= frequency

The table:

x , N , dx = ( x - A ) , N ∙ dx

200 , 142 , - 1200 , -170400

600 , 265 , - 800 , - 212000

1000 , 560 , - 400 , - 224000

1400 , 271, 0 , 0

1800 , 89 , 400 , 35600

2200 , 16 , 800 , 12800

--- , ΣN = 1343 , --- , Σ N∙dx = - 558000

x̄ = A + ΣN∙dx / ΣN

x̄ = 1400 + ( - 558000 ) / 1343 =

1400 - 558000 / 1343 =

984.5123 ≈ 985 m