The document defines common statistical terms used to describe data distributions, including measures of central tendency (mean, median, mode), measures of variability (range, average deviation, variance, standard deviation), and how to construct a frequency distribution table from raw data by grouping values into classes and calculating frequencies. Key steps covered are determining the number of classes, class boundaries, frequencies, and how to find the mean, median, mode from the frequency distribution table.
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