Introduction
This is a report on the use of measures of central tendency to determine overall performance. The measure of central tendency that should be used for a scenario is discussed. Measures of central tendency which are carried out for this purpose include the mean, maximum, minimum, range, standard deviation, range, median, variances, and the modes. These measures of central tendency are carried out on the scores in a quiz that had 15 students. The marks represent the marks that each student scored.
Measures of central tendency
The maximum mark that was scored in the quiz was 24 while the minimum was 4. This implies that the scores in the quiz have a range of 20 marks. The average and the median are valued at 16.6 and 17. The distance between the mean and median is very close. The most common mark that was scored by the students was 17 marks.
In these data set the values of the mean, median, and mode are very close. The close proximity between these values leads to the conclusion that there are no outliers in the data. For this instance where the values are close, the mean is the best measure of central tendency to use when gauging performance (Manikandan, 2011). However if the values from the score had a huge difference between the mean and median, the best measure of central tendency to use is the median (Wilcox & Keselman, 2003). A huge difference between the three values may lead to the conclusion that the scores contain outliers.
Variability is defined as the variance of values from the mean. The difference between the highest and fewest marks is 20. The variance in the quiz scores is 23.57 while the standard deviation has a value of 4.855. The variance is relatively high. Compared to the minimum values, the resulting standard deviation from the variance is valued at 4.855. These values indicate high variability and therefore have a high divergence from the mean. One of the major uses of variability scores is the determination of the distribution that is followed by the data (David, 1998). The distribution describes whether the sores in the test are clustered together or highly spaced. For this instance where the data set is small, the variability comes in handy because it measures how well the entre distribution is affected represented by an individual score.
A population is a set of instances of people or experimental units that possess some common characteristic (Nayak, 2010). A sample is a subset of experimental units selected from the population in such a way that it represents the characteristics of the total population. The number of experimental units in the sample is smaller than the number in the population. This is because the sample is only a subset of the population. Basically the population includes all elements of a data set. For the population only parameters can be calculated but for the sample, statistics can be calculated to analyze properties of the sample.
Conclusion
From the results of analyzing the data, the distribution of the marks is relatively fair. There is no student who scored extra-ordinary marks in the test. The average mark that was scored by the students is 16.6 marks. However, many students score a mark that highly varies with the average score of the total population. A sample represents the characteristics of a population and can be analyzed for statistical measures.
References
Wilcox, R. R., & Keselman, H. J. (2003). Modern robust data analysis methods: measures of central tendency. Psychological methods, 8(3), 254.
Manikandan, S. (2011). Measures of central tendency: Median and mode. Journal of pharmacology and pharmacotherapeutics, 2(3), 214.
Nayak, B. K. (2010). Understanding the relevance of sample size calculation. Indian journal of ophthalmology, 58(6), 469.
David, H. A. (1998). Early sample measures of variability. Statistical Science, 368-377.