standard deviation is a measure of precision or how well individual measurements agree with each other. The formula is:
where x1, x2 and x3 are the induvidual measurements; x(bar) is the mean and n is the nuimber of measurements.
Cumulative frequency curve like the standard deviation, is a good way to measure dispersion.
It is obtained by adding up the frequencies as you go along, to give a 'running total'.
Plot the cumulative frequency as the y-axis and the interval or measurements in the x axis.
When looking at a cumulative frequency curve, you will need to know how to find its median, lower and upper quartiles, and the interquartile range.
By drawing horizontal lines to represent 1/4 of the total frequency, 1/2 of the total frequency and 3/4 of the total frequency, we can read estimates of the lower quartile, median and upper quartile from the horizontal axis.
The interquartile range is the difference between the lower and upper quartile.
The box and whisker plot on the other hand is used to display information about the range, the median and the quartiles. It is usually drawn alongside a number line. Below is an example