The mean, median and mode are all valid measures of Central Tendency but, under different conditions, some measures of central location become more appropriate to use than others. Here we will learn about

Mean = ( sum of all observations) / Number of observations

In a discrete frequency distribution the arithmetic mean may be computed by any one of the following methods :

2) Short- cut method

3) Step- Deviation method.

4) Merits and Demerits of Mean

1) A batsman score the following number of runs in 6 innings :

36,35,50,46,60,55. Calculate the mean runs scored in an inning.

Mean runs scored = ( 36 + 35 + 50 + 46 + 60 + 55) / 6 = 282 / 6 = 47

∴ Mean runs scored in an inning is 47.

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2) If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Find the mean of 1st three observations.

Mean = ( sum of all observations) / Number of observations

11 = [x + ( x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5

55 = x + x + 2 + x + 4 + x + 6 + x + 8

55 = 5x + 20

5x = 35

∴ x = 7

Mean of 1st three observations,

= [ x + (x + 2) + (x + 4) ] / 3

= ( 3x + 6) / 3

= 3 (x + 2) / 3 = x +2 = 7 + 2 = 9

∴ mean of 1st three observations is 9.

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3) The mean of 40 observations was 160. It was detected on re-checking that the value 165 was wrongly copied as 125 for computation of mean. Find the correct mean.

n = number of observations = 40 and Mean = 160

∴ Mean = ( sum of all observations) / Number of observations

⇒ 160 = ( sum of all observations) / 40

⇒ 160 x 40 = sum of all observations

Thus, incorrect sum of observations = 160 x 40 = 6400

Correct sum of observations = Incorrect sum – incorrect observation + correct observation

⇒ correct sum of observations = 6400 – 165 + 125

⇒ correct sum of observations = 6360

∴ correct mean = correct sum of observations / Number of observations

⇒ = 6360 / 40 = 159

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