# Measures of Central Tendency

## Mean and Median

Statisticians use summary measures to describe the patterns of the collected data. Measures of central tendency indicate the most ‘typical’ value in a set of data collected for statistical analysis. The two most common measures of central tendency are the “mean” and the “median”. The mean value of a sample is computed by adding all the observations and dividing by the total number of observations involved in the data (Stattrek). The median of a sample data is the middle value of the observations when arranged in order from the smallest to largest values. If the sample data contains odd number of observations, the median is the middle value and when the data set contains even number of observations the median is arrived at averaging the two middle values.

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As measures of central tendency mean and median, carry advantages and disadvantages. The median value is considered a better indicator of the most typical value of a set of data. This measure can be applied when the set of data has an outlier or an extreme value, which differs greatly from the other values included in the set of data. On the other hand, if the data set contains large number of observations mean is considered as a better measure of central tendency.

## Standard deviation

Standard deviation is a statistical measure that describes how tightly all the various observations in a sample are clustered around the mean value in a set of data. When the observations in a sample are clustered the shape of the bell-shaped standard deviation curve is steep, the standard deviation of the data can be said to be of a smaller value. When the observations are scattered widely the curve will tend to be more flatter which indicates that, the standard deviation is large. The standard deviation is the measure to find out how close the different values in a data set are clustered around the mean value (Niles, 1995).

## Conclusion

Arithmetic mean is accepted universally as a measure of central tendency, based on the fundamental property of the measure, which is best in the least square sense. In fact, this is the criterion used by most of the statisticians while they derive values of the general linear model. Though the mean value carries the advantage of minimizing the squared distances between the other values of the distribution, median is the best measure as it minimizes the distances between other values of the distribution and itself. It should be noted that when the data is distributed symmetrically one could observe the mean and median coincide with each other.

In the case of symmetric distribution, both the distances and the squared distances from the center of the distribution are small. When the distribution is asymmetric, the median is considered as the best measure of central tendency (Visualstatistics).

For the data presented by the study, the mean value is 10.75 weeks. The median is calculated as 8.5 (taking the average values of 8 and 9 being middle observations). The standard deviation is 11.02. These statistics indicate that the data is asymmetric as the standard deviation is large and the mean and median values are not close enough. Therefore, it is unwise to use the mean value as the statistical indicator for considering the any further distribution of grant.

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The median is the best measure that needs to be considered in this case. Since the median value of 8.5 weeks is less than the confirmed value of 9.6 the innovative new treatment cannot be considered as better one. Moreover, the standard deviation of 11.2 is much higher than the established standard deviation of 3.2. This implies that the samples are distributed asymmetrically and therefore only median value is to be considered as the best for any consideration of further grant.

Niles, R. (1995). Standard Deviation. Web.

Stattrek. (n.d.). Statistics: Measures of Central Tendency. Web.

Visualstatistics. (n.d.). Measures of Central Tendency. Web.

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