What is a SYMMETRIC versus SKEWED DISTRIBUTION, give an example?

Solutions

Expert Solution

Distribution of data can be symmetrical or skewed, depending upon the nature of the data. A data distribution is symmetrical when its mean and median is equal to each other. Besides, in a unimodal distribution, the mean, median and mode will be same and equal to be symmetrical. But, in in skewed data distribution, the mean and mode will not be equal. A skewed data distribution, there can be positively skewed (having skewed to the right) and negatively skewed (having skewed to the left) distribution. When distribution is positively skewed, then mean is greater than median and median is greater than mode. If distribution is negatively skewed, then mean will be lower than the median and median is lower than mode. Besides, symmetric distribution forms the mirror image if divided into two halves, but it is not the case with skewed distribution. It can be understood by the following distributions.

The first distribution is 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 10. It is symmetrical distribution. Here, mean and median is 7.

The second distribution is 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8. It is negatively skewed. Here, mean is 6.45 and median is 7.

The third distribution is 6, 6, 7, 7, 7, 7, 8, 9, 10. It is positively skewed. Here, the mean is 7.44 and median is 7.

Graphical representations are as follows:

keosha answered 11 months ago

Next > < Previous

Related Solutions

For each of the following, determine whether the distribution described is more likely skewed right, skewed left, or relatively symmetric.

For each of the following, determine whether the distribution described is more likely skewed right, skewed left, or relatively symmetric.Number of sick days in the GC student populationSalaries for all players in the NFLNumber of cars owned per American citizenHeights of all females in the GC population

For each of the following, state whether you expect the distribution to be symmetric, right skewed,...

For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning. -Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below...

For the following data sets, are the samples positively skewed, negatively skewed or approximately symmetric? (You...

For the following data sets, are the samples positively skewed, negatively skewed or approximately symmetric? (You can use R to justify your answer.) (a) A = {0.9961905,0.9493184,0.8332006,0.9513567,0.9856061,0.9136707,0.9706223, 0.6834221, 0.8527071, 0.8052218, 0.9798628, 0.9862662}. (b) B = {0.256907054,0.371948965,0.302661234,0.245459145,0.488603820,0.435416721, 0.203228122, 0.004436282, 0.115262446, 0.058988085, 0.256066243, 0.141507075}. (c) C = {0.139061819,0.025883617,0.096332657,0.115620817,0.274004925,0.059080122, 0.072580116, 0.008576388, 0.068673036, 0.379232748, 0.117313230, 0.086692960}.

Example of a situation where a data set might be negatively skewed. Do the same for a positively skewed distribution.

Example of a situation where a data set might be negatively skewed. Do the same for a positively skewed distribution. As this is a discussion, check the other answers first to make sure your answer isn't already taken. If necessary, explain why the skews might be the way they are.

what distribution is referred to as approximately symmetric

Brainstorm an example of a skewed data distribution relating to something in real life. For your...

Brainstorm an example of a skewed data distribution relating to something in real life. For your example would the median be a better description of the center of the distribution, why or why not? What could be the ramifications of the MEAN being communicated to the audience instead of the median? Can you think of any situations where the data may be skewed and the mean communicated not the median? Textbook : Garfunkel, S. (2016). For all practical purposes: Mathematical...

A SYMMETRIC distribution with TWO parameters. A SYMMETRIC distribution with ONE parameter used when the population...

A SYMMETRIC distribution with TWO parameters. A SYMMETRIC distribution with ONE parameter used when the population standard deviation is unknown. A NORMAL distribution with mean 0 and standard deviation 1. The distribution of a sample statistic. Gives the NORMALITY of sample means for large sample. Using data to determine properties of population parameters. A single value used to estimate a population parameter. A z-score determined by the probability (1-Confidence Level/100)/2 t-distribution PARAMETER equal to n-1, where n the the sample...

Describe the Erikson's stage of intimacy versus isolation and give an example of what a person...

Describe the Erikson's stage of intimacy versus isolation and give an example of what a person might go through in experiencing this stage of life.

What is overmatching versus undermatching? Give an example of overmatching and undermatching (with hypothetical proportions) that...

What is overmatching versus undermatching? Give an example of overmatching and undermatching (with hypothetical proportions) that might occur on a concurrent VI 20-sec VI 30-sec schedule (which means that you must first work out the expected proportions with these schedules).

What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is...

What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is used in a real-world scenario. Write a one to two (1–2) page short paper in which you answer the questions about distribution sampling.

Subjects