MEASURES OF CENTRAL TENDENCY - Assignment Example

From both excel, and the formulae, the mean is 50.8, which is different from the mode and the median, which are 58 and 57, respectively. However, the figures are roughly close to each other showing that is spent over 50 minutes everyday in physical fitness activities. The numbers are lower than I expected since I work out for a whole hour every day. This means that I spend a couple of minutes in switching from one activity to another. The time I spend in switching from one activity to another and the time I spend on different physical fitness activities add up to sixty minutes per day.

The most effective measure of the central tendency, as far as the mean, median, and mode is the mean. This is because of the fact that it utilizes 100 percent of all the data in the sample (Walpole, 2010). The other measures of central tendencies, including the median and mode do not utilize all the information provided. Mean helps in performing further mathematical calculations thus helping in conducting more statistical tests. For example, it helps in the calculation of standard deviation, variances, as well as, significance tests.

Additionally, it has an algebraic definition (Bertsekas, 2002). The mean is applicable in the probability theory to generate probability distributions. Such distributions do not utilize other measures of central tendencies including the median and the mode. Mean as well has some weaknesses, for example, the presence of outliers in the data lowers its accuracy. Its strengths, as a measure of central tendency, outweigh its weaknesses. To draw the box plot, one utilizes the 25th percentile, the 50th percentile, and the 75th percentile.

The 25th percentile is the lowest score, which is greater than 25 percent of the scores. Using excel, the 25th percentile is 41. This means that the highest figure of the first 25 percent of the data is 41. The 50th percentile is equal to the median.