Mean and standard deviation

• Normal distributions have the same basic shape but can differ in their maximum height and width
• The mean is useful but fails to take into consideration the variation of values within a sample
• The standard deviation has to be calculated to find the spread of measurements about the mean of the normal distribution
• If the standard deviation is large the measurements are more spread about the mean, meaning it is not as reliable
• 95% of the data points of the sample will be in between 2 standard deviations of the mean
• Standard deviation allows for statistical analysis as it can test whether differences between two or more sets of data are statistically significant or not
• 68% of the data points are within 1 standard deviation of the mean
• If the error bars do not overlap, there is a statistical significant difference between the mean of two or more sets of data and the difference is not due to chance
• If the error bars overlap, there isn't s significant statistical difference between the mean of the two sets of data and the difference is due to chance