Mean and standard deviation
The median is known as a measure of location; that is, it tells us where the data are. As stated in , we do not need to know all the exact values to calculate the median; if we made the smallest value even smaller or the largest value even larger, it would not change the value of the median. Thus the median does not use all the information in the data and so it can be shown to be less efficient than the mean or average, which does use all values of the data. To calculate the mean we add up the observed values and divide by the number of them. The total of the values obtained in Table 1.1 was 22.5 , which was divided by their number, 15, to give a mean of 1.5. ...view middle of the document...
The Normal distribution is represented by a family of curves defined uniquely by two parameters, which are the mean and the standard deviation of the population. The curves are always symmetrically bell shaped, but the extent to which the bell is compressed or flattened out depends on the standard deviation of the population. However, the mere fact that a curve is bell shaped does not mean that it represents a Normal distribution, because other distributions may have a similar sort of shape.
Many biological characteristics conform to a Normal distribution closely enough for it to be commonly used - for example, heights of adult men and women, blood pressures in a healthy population, random errors in many types of laboratory measurements and biochemical data. Figure 2.1 shows a Normal curve calculated from the diastolic blood pressures of 500 men, mean 82 mmHg, standard deviation 10 mmHg. The ranges representing [+-1SD, +12SD, and +-3SD] about the mean are marked. A more extensive set of values is given in Table A of the print edition.
The reason why the standard deviation is such a useful measure of the scatter of the observations is this: if the observations follow a Normal distribution, a range covered by one standard deviation above the mean and one standard deviation below it
includes about 68% of the observations; a range of two standard deviations above and two below () about 95% of the observations; and of three standard deviations above and three...