Question #59284

Let $c$ be the minimum value of the quadratic expression $Q(t) = \frac{1}{2}t^2 - 4t + 20$. A continuous frequency distribution has exactly three classes of equal width $c$, with the lowest class interval starting at $0$. Let $S$ be the set of all real roots of the equation $(x^2 + x)(x^3 - (e+e^2+e^3)x^2 + (e^3+e^4+e^5)x - e^6) = 0$ The frequencies $f_1, f_2, f_3$ corresponding to the three classes (in increasing order of the class intervals) are the valid, real values of $\ln(\alpha)$ for $\alpha \in S$, sorted in strictly increasing order. Find the mean deviation about the mean for this frequency distribution.