Prepared by: Nurazrin Jupri

differences will be large differences will be small MATH0102|Nurazrin Jupri

 Two groups of three students Group Group  Mean mark Group = 21/3 = 7 Group = 21/3 = 7  Same mean mark, but Group 1’s marks are widely spread, Group 2’s are all the same  The following diagram reinforces this point MATH0102|Nurazrin Jupri

 A measure of the average amount by which the values in a distribution (x) differ from the arithmetic mean  Average of the absolute deviations from the arithmetic mean (ignoring the sign) MATH0102|Nurazrin Jupri

grouped ungroupe d Vertical bars = all differences are taken as positive MATH0102|Nurazrin Jupri

 X 1 = 2, X 2 = 4, X 3 = 3  MD =  MD = = = ⅔ MATH0102|Nurazrin Jupri

Mean Deviation of grouped data X MATH0102|Nurazrin Jupri

 If we square all the deviations from the arithmetic mean, then we no longer need to bother with dropping the signs since all the values will be positive.  Variance is the average of the squared deviations from the arithmetic mean MATH0102|Nurazrin Jupri

 Variance =  To calculate the variance 1. Calculate the mean value 2. Subtract the mean from each value in turn, that is, find 3. Square each answer to get MATH0102|Nurazrin Jupri

4. Add up all these squared values to get 5. Divide the result by n to get 6. You now have the average of the squared deviations from the mean (in square units) MATH0102|Nurazrin Jupri

 This is simply the square root of the variance  An advantage is that we avoid the square units of the variance  Larger SD, larger the average dispersion of data from the mean  Smaller SD, smaller the average dispersion of data from the mean MATH0102|Nurazrin Jupri

xixi x 1 - x(x 1 – x) Total 4 – 7 = – 7 = 0 10 – 7 = 3 (-3 2 ) = = = 9 18 MATH0102|Nurazrin Jupri

Variance = square units Standard deviation is square root of 6 = units MATH0102|Nurazrin Jupri

xixi x i - x(x i – x) 2 7 Total 7 – 7 = = 0 0 MATH0102|Nurazrin Jupri

Variance = square units Standard deviation is square root of 0 = 0 i.e. there is no spread of values MATH0102|Nurazrin Jupri

where Fi = Frequency of ith class interval Xi = mid point of ith class interval j = number of class intervals MATH0102|Nurazrin Jupri

LCB UCB FXFXFX^ MATH0102|Nurazrin Jupri

S 2 = 174 – S 2 = 174 – S 2 = S = √ = MATH0102|Nurazrin Jupri