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By Pearn W. L., Lin G. H.

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In full these were as follows. 3000 200 1250 15 75 4500 3500 4000 1200 35 30 300 60 75 50 120 250 10 400 1200 150 2400 250 1500 140 50 250 45 250 25 5 450 It is clear that there is considerable spread in the data. It is continuous data and the reporter is aware that they appear to have been rounded but he does not know to what level of precision. Consequently there is no way of reflecting the level of precision in setting the interval boundaries. 27 S1 1 Exploring data The reporter wants to estimate the mean and decides on the following grouping.

1. 7 goals. 41), we see that Joe’s goal scoring is more consistent (or less variable) than Kim’s. This confirms what was found when the mean absolute deviation was calculated for each data set. 2). An alternative form for the standard deviation The arithmetic involved in calculating ∑(x − x )2 f can often be very messy. An alternative formula for calculating the standard deviation is given by ●● standard deviation = ∑x 2f n − x 2 or ∑x 2f ∑f − x2 37 S1 1 Exploring data Consider Joe’s data one more time.

In quality control this can be an advantage as it is very sensitive to something going wrong on a production line. Also the range is easy to calculate. However, usually we want a measure of spread that uses all the available data and that relates to a central value. Measures of spread (variation) ! One of the problems with the range is that it is prone to the effect of extreme values. S1 1 The mean absolute deviation Kim and Joe play as strikers for two local football teams. They are being considered for the state team.

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A Bayesian-like estimator of the process capability index Cpmk by Pearn W. L., Lin G. H.

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