Positively and Negatively Skewed or Normal Order Instructions: I don’t need any references, just an answer for each of the six examples given.
Please state whether they are positively skewed, negatively skewed, or normal. And just a very brief explanation why for each.
Positively and Negatively Skewed or Normal Sample Answer
- Income:
Positively skewed: This is mainly because income is bounded below usually by minimum income, with low-income levels being plausible, yet very large maximum income is very well known to occur (mostly in extents of magnitude higher values), with a significant number being in the middle making the difference between minimum income and maximum income levels extremely varied which is characterized by long tail on the positive side of the skew.
- Mileage on used cars for sale:
Positively skewed: This is mainly because income is bounded below usually by minimum mileages, with low mileage being plausible, yet very large maximum mileages are very well known to occur (mostly in extents of magnitude higher levels), but most of the mileages lying within the middle region of the distribution which is characterized by long tail on the positive side of the skew.
- House prices:
Positively skewed: This is mainly because income is bounded below usually by minimum prices, with low prices being plausible, yet extremely high prices are very well known to occur, but a significant number of prices being in the middle making the difference between minimum income and maximum prices extremely varied which is characterized by long tail on the positive side of the skew.
- Scores on an easy test:
Normally distributed: This is attributed to the fact that an easy test provides a random measure of students’ knowledge in which a similar platform is universally applied meaning that there is no outside influence to interfere with scores.
- Scores on a test that students are motivated:
Positively skewed: This is because the students will tend to score higher due to the available motivation which might be informed of reward attributable to the extra effort put by the students in order to get the reward.
- Age at death in developed countries:
Negatively skewed: This is because most national statistical agencies do not conclusively cover the extremely old ages in their age bins, where for instance most of them go up to between 95> or 100> years yet there are older people making the final bin uncomfortably wide hence resulting to negative skew.
