Question

Describe the difference you would expect to see in the values of the mean and median for

a normal distribution, a positively skewed distribution, and a negatively skewed

distribution.

Answer 1

The above curve is bellshaped curve or normal curve or gaussian curve or symmetric curve.The normal distribution gives this curve and in this curve the frequency gradually increases from lower extreme value then stop at one  point and then gradually decreases to upper extreme value from that point.Here one point is mean, meadian and mode to that data set. That one point gives mean value to that total data and middle value to that data and highest valu to that data.For example Height,Weight,Marks of a students in a class etc...Here The height of a person gradually increases since from his birth and then at some stage he maintain his average for some years in his life after his aveage life time is expired then height gradually decreases till his death. For suppose the students having minimum and maximum  marks are less in class.

For eg: 4; 5; 6; 6; 6; 7; 7; 7; 7; 7; 7; 8; 8; 8; 9; 10 observe the data,in this data Mean = 7, median =7 and Mode =7.The data is an example for normal distribution data.

Skewness means lack of symmetry.If the fruquency is plotted on the graph it doesnot give bell shaped curve.If the curve gives right tail then that data is positively skewed And the tail is on left side then that data is negatively skewed

In skewed ditribution mean,median and mode are not equal.There is a relation

Postively skewed distribution the relation between mean,median and mode is mean > median> mode

For example :

X	Frequency
1	70
2	50
3	30
4	15
5	8
6	5

In negatively skewed distribution the relation between mean,median and mode is mean < median< mode

X	Frequency
1	3
2	9
3	18
4	25
5	30
6	50