Question

Give examples of three variables that have different distributions (bell-shaped, skewed left and skewed right). Explain your answer.

Give examples of two variables that would have different spreads (one that has a close spread and the other that has a wide spread). Explain your answer.

“Please Provide a real life example that pertains this question “

Answer 1

(1)

Real life example of a variable X that has bell shaped Distribution:

Distribution of a quality characteristic, say radius of O ring, of a manufactured item.

It will have a value of mid value = desired characteristic and with allowable tolerance on either side.

(2)

Real life example of a variable X that has skewed left Distribution:

Distribution of house hold income in the U.S. is skewed left with a long left tail. The mean is to the left of the peak.

(3)

Real life example of a variable X that has skewed right Distribution:

If a test conducted in a school has a high difficulty level, then most of the students will have a poor - to average performance in it. This bulk of students will form the maximum part of the distribution, towards the left side of the positively skewed distribution curve. The highest mark in the test will be obtained by only a few meritorious students, which formd the right tail of extreme values. The students with very high marks will shift the mean towards the right, making it a positively skewed distribution. There will be a higher frequency of low scores and a lower frequency of high scores.

(4)

Example of low spread:

Because of strict quality control, the distribution of a quality characteristic in an industry will have low spread.

(5)

Example of wide spread:
The distribution of age of persons in a place will have wide spread because the place can have small children and also very aged people.