# Measures of Center Discussed

Measures of Center Discussed

St. Thomas University

STA 2023

Dr. Freddy Suarez

03/23/2023 The central position of a set of numbers is represented by its mean. It is calculated by adding the values of all the individual observations’ measurements (Urdan, 2022). As a first step in calculating the mean, a set of numbers is sorted, and the middle number is identified (James et al., 2013). The average, or mean, of a group of numbers, is calculated using arithmetic. In this way, the mean locates the midpoint between all measurements. We take the following set of data for the marks scored by 9 students in a certain test: 12, 16,18,15,16,17,19,16 and 15. We add the marks for each student and divide them by the number of students. The total marks are 150 divided by 9 students which give a mean of 16.667 marks.

One can find the value that roughly divides the data in half using the median. This means that 50% of the observations fall below the median, and 50% fall above it (Urdan, 2022). With a set of data with an odd number of observations, the median represents the midway number (Urdan, 2022). Thus, by sorting the observations according to the measurement, the median locates the most central observation in statistical data. Using the above example, we arrange the data in an ascending order as follows: 12, 15, 15,16,16,16,17,18,19 and take the middle number to be the middle number as the median of the data. In this case 16 is the median of the data.

The center of the data set is represented by the mode, which is based on the frequency distribution of the observations (Urdan, 2022). In order to determine which data value occurs

most frequent, we first count how often each value occurs. As a result, the most common occurrence(s) are the modes and a measure of center (James et al., 2013).In this case the number occurring most is 16 which appeared three times.

The mathematical definition of the midrange is the midpoint between the highest and lowest values found in a set of measurements. It is determined by adding the smallest and largest numbers and dividing by 2, yielding the median. Therefore, the midrange can roughly estimate the observation’s centre based on the data’s extremes. In this case the lowest and the highest numbers are 12 and 19 respectively. We add them to get a midrange of 15.5 marks.

References

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, p. 18). New York: springer. ISBN: 978-1-0716-1418-1

Urdan, T. C. (2022). Statistics in plain English. Taylor & Francis. ISBN 9781138838345

Measures of Center Discussed