Standard Deviation
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What is “standard deviation?”
• Spread of data about the mean value.
Why is standard deviation more useful than calculating the range of data? 3 main reasons!
1.) SD shows spread of data from the mean, whereas, range is only difference between the highest/ lowest value. 2.) SD reduces the effect of anomalies whereas, range includes anomalies. 3.) SD can be used to indicate whether a difference between results is significant.
Why would standard deviation be useful for making a conclusion from data?
• Overlaps between SD, shows that there is likely to be significant difference between the mean values. • No overlap between SD shows that it is likely there is NO significant difference between the mean values.
Past paper 1 2023 Mean diameter of clear zone = 1.) 16.6, standard deviation is +/-2.4 2.) 13.4, standard deviation is +/-2.2 Use this information to consider whether the differences in means are liklely due to chance. Explain using at least 1 calc.
• SD’s overlap so likely difference is due to chance. • Calculations: 16.6 +/- (2x2.4) = 11.8 –> 21.4 13.4 +/- (2x2.2) = 9–> 17.8
How do you work out the RANGE of values from standard deviation and mean, when standard deviations are +/-2 over 95% over data?
• Mean +/- (2 x standard deviation for particular mean.) the number you multiply standard deviation by would be different for the value given in the Q