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Answer:
Step-by-step explanation:
Given
Required
Write a recursive expression
When n = 1
When n = 2
can be rewritten as
Substitute 3 for f(1)
Express 1 as 2 - 1
----- (1)
When n = 3
can be rewritten as
Substitute 8 for f(2)
Express 2 as 3 - 1
------ (2)
Write out (1) and (2)
Replace 2 and 3 with n in both cases; This gives
Hence;
The recursive is
The answer is 7.9306
Using the formula in the attached:
Where: xi = sample value; μ = sample mean; n = sample size
1.) Calculate the mean first:
μ = 12.0 + 18.3 + 29.6 + 14.3 + 27.8 / 5
= 102 / 5
μ = 20.4
2.) Using the mean, calculate (xi - μ)² for each value:
(12.0 - 20.4)² = 70.56
(18.3 - 20.4)² = 4.41
(29.6 - 20.4)² = 84.64
(14.3 - 20.4)² = 37.21
(27.8 - 20.4)² = 54.76
3.) Sum the squared differences and divide by n - 1.
μ = 70.56 + 4.41 + 84.64 + 37.21 + 54.76
= 251.58 / 5-1
μ = 62.895 (this is now called sample variance)
4.) Get the square root of the sample variance:
√62.895 = 7.9306
Using the formula in the attached:
Where: xi = sample value; μ = sample mean; n = sample size
1.) Calculate the mean first:
μ = 12.0 + 18.3 + 29.6 + 14.3 + 27.8 / 5
= 102 / 5
μ = 20.4
2.) Using the mean, calculate (xi - μ)² for each value:
(12.0 - 20.4)² = 70.56
(18.3 - 20.4)² = 4.41
(29.6 - 20.4)² = 84.64
(14.3 - 20.4)² = 37.21
(27.8 - 20.4)² = 54.76
3.) Sum the squared differences and divide by n - 1.
μ = 70.56 + 4.41 + 84.64 + 37.21 + 54.76
= 251.58 / 5-1
μ = 62.895 (this is now called sample variance)
4.) Get the square root of the sample variance:
√62.895 = 7.9306