Standardised deviation test

[Aisha]

In solutions for chapter 10 practice questions, Q10.10(iii) , under ISD test, it's given that the distribution is positively skewed, which is not so good.
How did we come to a conclusion that it is positively skewed?
Also while we talk about symmetry, we tend to look at the number of positive and negative deviations which are 5 and 4 respectively in this case, so from this can't we conclude that it is fairly symmetrical?

 

[Andrew Martin]

Hi Aisha

We can consider both how many positive and negatives there are as well as the magnitudes of the deviations. Although there are similar counts (5 and 4 as you say), the negative ones are all in the (-1,0) range, where as the positive ones are somewhat spread from 0 to 3. We know that a normal distribution has symmetry in the magnitudes as well as the counts. This is also the same observation that leads to the conclusion of positive skew.

Andy

 

[Aisha]

Understood. Thank you!

Hi Aisha

We can consider both how many positive and negatives there are as well as the magnitudes of the deviations. Although there are similar counts (5 and 4 as you say), the negative ones are all in the (-1,0) range, where as the positive ones are somewhat spread from 0 to 3. We know that a normal distribution has symmetry in the magnitudes as well as the counts. This is also the same observation that leads to the conclusion of positive skew.

Andy