47. Mean from an FD X = Σ f i X i K i=1 Σ f i K i=1 where X i = class mark of the i th class
48. Median from an FD Md = LCB Md + C n/2 - <CF Md-1 where LCB Md = lower class boundary of median class <CF Md-1 = less than cumulative frequency preceeding the median class f Md
49. Mode from an FD Mo = LCB Mo + C f Mo - f Mo-1 where LCB Mo = lower class boundary of modal class f Mo , f Mo-1 , f Mo+1 = frequency of modal class, class preceding and class succeeding the modal class 2f Mo - f Mo-1 - f Mo+1
50. Mean Deviation from an FD MD = Σ f i |X i - X| n i=1 n where X i = class mark of the i th class n = total number of observations; total frequency, ie. n = Σ f i
51. Variance from an FD s 2 = Σ f i (X i - X) 2 n i=1 (n -1) where X i = class mark of the i th class n = total number of observations; total frequency, ie. n = Σ f i
52. Variance from an FD s 2 = n Σ f i X i 2 - ( Σ f i X i ) 2 n i=1 n(n -1) n i=1 where X i = class mark of the i th class n = total number of observations; total frequency, ie. n = Σ f i