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Key Notes, Chapter-14, Statistics, •, , Mean: The arithmetic mean (or, simply mean) is the sum of the values of all the observations, divided by the total number of observation., , •, , •, , The mean for grouped data can be found by:, , ∑ fixi, ∑ fi, , (i), , The direct method = X =, , (ii), , The assumed mean method X = a +, , ∑ fidi , Where, ∑ fi, , (iii), , The step deviation method: X = a +, , ∑ fiui, X −a, × h, where U l = i, ∑ fi, h, , d i = x i − a., , The mode for the grouped data can be found by using the formula:, ,  f1 − f 0 , mod e = l + ,  ×h,  2f1 − f 0 − f 2 , l = lower limit of the modal class., , f1 = frequency of the modal class., fo = frequency of the preceding class of the modal class., f2 = frequency of the succeeding class of the modal class., h = size of the class interval., Modal class - class interval with highest frequency., •, , The median for the grouped data can be found by using the formula:,  n / 2 − Cf , median = l + ,  × h, f, , , l = lower limit of the median class., n = number of observations.

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Key Notes, Cf = cumulative frequency of class interval preceding the median class., f = frequency of median class., h = class size., •, , Empirical Formula: Mode = 3 median - 2 mean., , •, , Cumulative frequency curve or an Ogive:, (i), , Ogive is the graphical representation of the cumulative frequency distribution., , (ii), , Less than type Ogive:, , •, , Construct a cumulative frequency table., , •, , Mark the upper class limit on the x = axis., , •, , (i), , More than type Ogive:, , (ii), , Construct a frequency table., , (iii), , Mark the lower class limit on the x-axis., , To obtain the median of frequency distribution from the graph:, (i), , Locate point of intersection of less than type Ogive and more than type Ogive:, , (ii), , Draw a perpendicular from this point on x-axis., , (iii), , The point at which it cuts the x-axis gives us the median.