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| Mean |
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| Mean is the arithmetic average. |
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| It is obtained by adding the raw scores and dividing the sum by the number of items. |
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| Suppose the raw scores are |
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| x1, x2, x3,…, xN |
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then, mean  |
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  |
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| where M = mean |
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| x = each score or item |
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| N = number of items |
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 = sigma, which means 'summation of ' |
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| Find the mean of 6, 10, 4, 12, 8. |
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 M = 8 |
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| The weight in kg of the 9 members of a school tug-of-war team are: 54, 59, 63, 53, 73, 49, 50, x, 45. |
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| If the average weight is 56 kg, find x. |
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  |
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 x = 58. |
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| There are three methods to find mean for a frequency distribution. |
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| (i) Direct method: |
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 |
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| where x is the mid-interval |
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| f is the frequency |
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| M is the mean |
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| (ii) Short-cut method: |
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| where A = assumed mean |
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| d = x - A |
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| (iii) Step-deviation method: |
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| where i = class size |
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| We illustrate each of these methods with the help of the following examples. |
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| Find the mean for the following table by the 'Direct Method' |
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| Calculate the mean marks in the distribution below by the 'Direct Method'. |
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| Direct Method: |
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 |
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| = 29.75 |
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| Calculate the mean of the question in example 4 by Short-Cut Method. |
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| Short-cut Method: |
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| (i) This method makes the calculations easy. |
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| (ii) We assume mean as A, one of the class-marks near the middle of the 'x' column. |
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| (iii) Then, an additional column d = x - A is formed. |
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| (iv) The mean is calculated by applying the formula. |
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| Assumed mean = A = 24.5 |
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M =  |
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| = 24.5 + 5.25 |
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| = 29.75 |
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| The answer remains the same by any method. |
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| Weights of 50 eggs were recorded as given below. Calculate their mean weight to the nearest gram by Step Deviation Method: |
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| Step - Deviation Method: |
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| Assumed mean = A = 97.5 |
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M =  |
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| = 97.5 - 1.6 |
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| = 95.9 |
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| = 96 gm |
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| Once you have mastered this method, statistical calculations become very easy. Large values of x are reduced to single digit numbers by Step-Deviation Method. |
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