Answer:
a₆ = 12
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂ = 5 and a₁₀ = 19 , then
a₁ + d = 5 → (1)
a₁ + 9d = 19 → (2)
Subtract (1) from (2) term by term to eliminate a₁
8d = 14 ( divide both sides by 8 )
d = 1.75
Substitute d = 1.75 into (1)
a₁ + 1.75 = 5 ( subtract 1.75 from both sides )
a₁ = 3.25
Then
a₆ = 3.25 + 5(1.75) = 3.25 + 8.75 = 12
Here is dependence between scores and x-values:
where 
is the mean, 
is standard deviation and i changes from 1 to 2.
1. When i=1, 
then
2. When i=2, 
then
Now solve the system of equations:
Subtract first equation from the second:
Then
Answer: the mean is 62, the standard deviation is 20.
In order to get the constant of variation, you can either
make a linear equation that relates x and y in which the slope is the constant
of variation
LINEARIZING
x = 3y
the slope of the equation is 3 and therefore the constant of
variation is 3
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