bus-stat-book1

G rice wheat and pulses are more important than tea

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Unformatted text preview: after giving proper weight to each group. Definition: The average whose component items are being multiplied by certain values known as “weights” and the aggregate of the multiplied results are being divided by the total sum of their “weight”. If x1, x2…n be the values of a variable x with respective x weights of w1, w2… n assigned to them, then w w x + w2 x2 + .... + wn xn ∑ wi xi Weighted A.M = x w = 1 1 = w1 + w2 + .... + wn ∑ wi Uses of the weighted mean: Weighted arithmetic mean is used in: a. Construction of index numbers. b. Comparison of results of two or more universities where number of students differ. c. Computation of standardized death and birth rates. Example 5: Calculate weighted average from the following data Designation Class 1 officers Class 2 officers Subordinate staff Clerical staff Lower staff Monthly salary (in Rs) 1500 800 500 250 100 99 Strength of the cadre 10 20 70 100 150 Solution: Designation Monthly salary,x 1,500 800 500 15,000 16,000 35,000 250 100 Class 1 officer Class 2 officer Subordinate staff Clerical staff Lower staff Strength of the cadre,w 10 20 70 wx 100 150 350 25,000 15,000 1,06,000 ∑ wx ∑w 106000 = 350 = Rs. 302.86 Weighted average, x w = Harmonic mean (H.M) : Harmonic mean of a set of observations is defined as the reciprocal of the arithmetic average of the reciprocal of the given values. If x1,x2… n are n observations, ..x n n 1 ∑ x i =1 i For a frequency distribution H.M = HM. = . N 1 ∑1 f x i= i n Example 6: From the given data calculate H.M 5,10,17,24,30 100 X 1 x 0.2000 0.1000 0.0588 0.0417 0.0333 0.4338 5 10 17 24 30 Total H.M = = n 1 ∑ x 5 0.4338 = 11.526 Example 7: The marks secured by some students of a class are given below. Calculate the harmonic mean. Marks 20 21 22 23 24 25 Number of 4 2 7 1 3 1 Students Solution: Marks X 20 21 22 23 24 25 No of students f 4 2 7 1 3 1 18 1 x 0.0500 0.0476 0.0454 0.0435 0.0417 0.0400 101 ƒ( 1 ) x 0.2000 0.0952 0.3178 0.0435 0.1251 0.0400 0.8216 N 1 ∑f x 18 = = 21.91 0.1968 Merits of H.M : 1. It is rigi...
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