Explain relative position of mean, median and mode in a normal distribution and skewed distribution with the help of diagram.

The three measures mean, median and mode of the central tendency could easily be compared with the help of normal distribution curve which is given below:

Fig. 2.4 : Normal Distribution Curve

The normal distribution has an important characteristic. The mean, median, mode are the same score because a normal distribution is symmetrical. The score with the highest frequency occurs in the middle of the distribution and exactly half of the scores occur above the middle and half of the scores occur below. Most of the scores occur around the middle of the distribution of the mean. Very high and very low scores do not occur frequently and are, therefore, considered rare.

If the data are skewed or distorted in some way the mean median and mode will not coinside and the effect of the skewed data needs to be considered in the following figure.

Fig. 2.5 : Positive Skew

Fig. 2.6 : Negative Shew