Answer:
12.83
Step-by-step explanation:
S = 12.091
N = 12
We must find the 12th point, X
The formula of S² (variance) as a function of µ (media) is as follows:
S² = (1/N Ʃ Xi²) - µ²
S² = 146.2
Multiplying both members by N,
N S² = Ʃ Xi² – N µ²
On the other hand,
µ = (25 + 41 + 49 + 25 + 30 + 13 + 31 + 34 + 27 + 54 + 38 + X) / 12
µ = (367 + X) / 12
Replacing,
12 x 146.2 = 13607 + X² – 12 (367 + X)² / 144
1754.4 = 13607 + X² – 0.0833 (134689 + 734 X + X²)
1754.4 = 13607 + X² – 11219.5 – 61.14 X – 0.0833 X²
0.92 X² – 61.14 X + 633.1 = 0
This is solved by finding the two values of X that satisfy the equation.
The solution requires solving the quadratic formula,
X12 = (-b ± √(b² - 4ac)) / 2a
The values are:
X1 = 12.83
X2 = 53.62
Since we know that the value is 25 or less, the answer is 12.83
