Skewness of data

[asmkdas]

The Question is taken from Assignment X1
Question X1.11 (iii)

The skewness is required here:

We got here Mean = 0.20 and Median = 0.157427
It has been said that since Mean is to the right of the Median hence the curve is positively skewed.

My point is that to know the skewness we need to get the Mode (Apex point of curve) anyhow and if the Mean is right of Mode then we'll get the positively skewed curve or vice versa. But the in book's answer nowhere Mode is defined, then how then said it like the curve is positively skewed.

Please explain.

 

[Tim.Sullivan]

In a symmetrical distribution curve the mean, median and mode will all be in the centre of the curve.

If the curve is skewed positively (to the right) we would expect:
- the mode is at the highest point in the curve
- the median is the "middle" value so will stay relatively close to high point of the curve, pulled slightly to the right (depending on the skew)
- the mean will be affected by the "outliers" and so will be "pulled" to the right more-so than the median.

In general for a positive skew the order will be 1. Mode 2. Median 3. Mean

In the example we're given that the mean is 0.2 and the median is 0.157. Then from the info above we can identify that the distribution is positively skewed without needing to know the mode.