Question 1
A measure of central tendency refers to a statistical value used to describe a population by identifying central positions within the dataset. The three measures of central tendency include mode, mean, and median. According to the Australian Bureau of Statistics (2020), the mean or arithmetic average refers to the sum total of values of every observation in a sample population divided by the total observations in the dataset. The median discusses to the central value in a sample population when the observations are organized in descending or ascending order. Another measure is the mode, which is the most frequent value within a population or dataset.
Question 2
A skewed distribution is one where data points are clustered more towards one side than the other. Positively skewed distribution refers to one that has a longer tail in the positive direction (“A Look at Skewed Distributions,” n.d.). This means that the measures of central tendency tend to cluster towards the right. For instance, income distribution represents positively skewed distributions, where a small number of people make millions of dollars. On the other hand, negatively skewed distribution refers to a longer tail distribution in the negative direction. For negatively skewed distributions, the measures of central tendency tend to cluster towards the left. For instance, a distribution on test grades where most students perform well, but few failed.
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Question 3
In a normal distribution, half of the distribution mirrors the other half. This distribution is symmetrical; therefore, it is not skewed. This distribution is significant and it is widely used in statistics. The measures of central tendency tend to cluster in the same position. For a normal distribution, the mode, median, and mean are equal (Lane, n.d.). This is because the distribution is weighted in the middle and less dense in the tails.
References
Lane, D., M. (n.d.). Introduction to Normal Distributions. http://onlinestatbook.com/2/normal_distribution/intro.html#:~:text=The%20mean%2C%20median%2C%20and%20mode,the%20standard%20deviation%20(%CF%83).
A Look at Skewed Distributions. (n.d.). http://www.cvgs.k12.va.us/DIGSTATS/main/descriptv/d_skewd.html
Australian Bureau of Statistics. (2020). Statistical Language - Measures Of Central Tendency. https://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+measures+of+central+tendency
