descriptive stats revisited

Last post I attempted a brief and somewhat unclear introduction to descriptive statistics. So by way of review I will summarize last post with a graph to help depict things. The three most basic ways of describing a data set are its average, spread and shape. These three concepts are very important as performing statistical analysis depends on these three descriptions of the data being "normal." The average of the data set represents where the majority of the data lie. A normally distributed set of data (referred to as a bell curve when plotted) will have an obvious mean at the peak of that curve. See how on the normal curve below, the line representing the mean divides the curve into two symmetric halves.

The spread of the data indicates to what degree all the data points vary away from the average. Standard deviation is a number that indicates the average distance of all data points from the average. Higher standard deviations indicate that the range of data spread further on either side of the average. See the lines on either side of the central average line on the graph below? The first line on either side of the average line indicates a point that is 1 standard deviation from the mean. The next line indicates a point that is 2 standard deviations away from the mean. Particular to the normal bell curve is the reality that 67% of all data will be only one standard deviation from the mean and 95% of the data only 2 standard deviations away from the mean.

The shape indicates whether the bell curve has a long tail to the left [negative skew], long tail to the right [positive skew], tall curve [leptokurtic], flat cruve platykurtic). Any distortion of the bell curve impacts statistical calculations as basic statistics assume a normal bell curve. See below for depictions of skewed data.

Next post I will answer the following question: how do we know if the difference between two groups or two measurements is due to chance or due to skill or treatment effect?