Average Value:

The summation symbol, Σ, introduced in the first chapter, is often used when dealing with the average value, x¯ .

Using the first example here, the average value could have been expressed in the following manner:

where:

x¯_car        =          the average value (cost) of a car

x_i         =          each of the individual car prices

N         =          total number of cars

In the right side of the above equation can then be rewritten.

x¯_car  = x₁ + x₂ + x₃ + x₄ + x₅ + x₆/6

Substituting the value 10,200 for x₁, 11300 for x₂, 9,900 for x₃, etc.

x¯_car  =     10,200 + 11,300+  9,900+  12,000+  18,000+  7600/6

x¯_car  = 11,500

Example:

If we were to apply the average value equation from above to the second example concerning temperature so how would it be written and what would be the values for N₁, x_i?

Solution:

x₁  = 600

x₂  = 596

x₃  = 597

x₄  = 603

x¯_temp   = x₁ + x₂ + x₃ + x₄/4

(600 + 596 +597 + 603)/4

=          599