Question

Good Luck. (Need to show all your work to get full credit; no work, no credit) 1.For the given sample data below: a Construct a frequency distribution using six classes for a sample data that includes. Class Limits (5 pts), Class Boundaries (6 pts), Frequency (3 pts), Relative frequency (3 pts), Cumulative Frequency (3 pts), Midpoint X.5 pts), f-x-(5 pts), f. (6 pts). b. For constructed grouped data find: mean (8 pts), mode for grouped data (2 pts), modal class (2 pts), the variance (10 pts), and the standard deviation (2 pts) c. Draw histogram and discuss the shape of a distribution (10 pts), frequency polygon (10 pts) ogive (10 pts), and pie chart for the following table (10 pt). NOTE: you MUST use 2.0 as a lower limit of the first class and do appropriate estimation for class width and in other computations. 4.6 3.9 2.8 6.6 4.2 3.7 3.7 5.9 3.2 2.2 3.2 4.1 21 4.2 50 46 54 24 63 29 5.3 40 4.7 3.6 3.3 6.9 45 2.5 5.4 5.7 3.84.1 7.96.2 3.0 33 5.0 5.4 3.4 4.4 4.0 365.0 4.1 48 72 64 30 3.5 53 7.7 3.9 26 5.6 33 55 43 3.9 63 3.1 3.1 3.0 4.8 4.1 5 Class Limits Class boundaries Tally Frequency Relative CumuativeClas Frequency regueny

Answer 1

a.

b. Mean=280.35/63=4.45

Modal class=2.95-3.95

$Mode=x_l+\frac{f_m-f_{m-1}}{2f_m-f_{m-1}-f_{m+1}}\times c\\ where,~x_l=lower~class~boundary~of~modal~class=2.95\\ f_m=frequency~of~modal~class=19\\ f_{m-1}=frequency~of~preceding~class~of~modal~class=7\\ f_{m+1}=frequency~of~succeeding~class~of~modal~class=16\\ c=class~width~of~modal~class=1\\ then~Mode=3.75.\\ Variance=1357.5575 /63-(4.45)^2=1.7460\\ Standard~deviation=\sqrt{1.7460}=1.3214$

(c)

Hence shape of the distribution is positively skewed.

7.9 2.1 5.8 Maximum Minimum Range No. of classes- Class width- Class limit Class boundaries Frequcy(f) Relative frequency Cumulative frequency Mid value(xm) f*xm f*xm 2 2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 7.0-7.9 1.95-2.95 2.95-3.95 3.95-4.95 4.95-5.95 5.95-6.95 6.95-7.95 Total 17.15 42.0175 19 16 0.3016 0.254 0.1905 26 3.45 65.55 226.1475 4.45 5.45 6.45 7.45 65.4 356.43 38.7 249.615 22.35 166.5075 280.35 1357.558 0.0476 63 Histogram Frequency polygon 18 16 14 14 완8 1.95-2.95 2.95-3.95 3.95-4.95 4.95-5.95 5.95-6.95 6.95-7.95 1.95-2.95 2.95-3.95 3.95-4.95 4.95-5.95 5.95-6.95 6.95-7.95 Class boundary Class boundary Pie Chart Ogive 1.95-2.95 2.95-3.95 3.95-4.95 4.95-5.95 5.95-6.95 6.95-7.95 5% 11% 10% 1996 30% 25% 1.95-2.95 2.95-3.95 3.95-4.95 4.95-5.95 5.95-6.95 6.95-7.95 Class boundary