Which Measure is a Better Measure of Typical Value, Mean or Median?
It is often difficult to determine which value would best measure the typical value of a data set. Typically, if the data within the data set is tightly grouped, and thusly, very close together with regard to value, then the mean will likely be the best measure of the typical value (Sullivan, 2007). In contrast, if there are one or more outliers within the data set, which are extreme values that are either much larger or much smaller than the rest of the numbers in the data set, the median will often provide a more accurate measure of typical value among the data set (Sullivan, 2007). A review of research with regard to cholesterol treatment has reviewed an interesting point. In most cases, researchers take into account both the mean and median values in order to come up with a more accurate value that can be used to interpret research findings. Insull et al. (2003) from the Mayo Clinic used both the mean and median to describe the total decrease in cholesterol levels among patients within the study (Insull Jr., et al., 2001). As a result, when the interpretation of the data set is more complex, such as it is in this case, the use of both mean and median as a measure of typical value can help to further enhance the accuracy of the true typical value among the data set.
Which Measure is a Better Measure of Dispersion, Standard Deviation or the Interquartile Range?
The range refers to the difference between the largest and the smallest values within a particular data set (Manikandan, 2011). Both standard deviation and interquartile measurements seek to determine the dispersion of a data set. The interquartile attempts to measure dispersion by calculating the difference between the 25th and 75th percentile (1st and 3rd quartile). In contrast, standard deviation, which is the most commonly used measure of dispersion, calculates the spread of the data within the data set as it falls around the mean (Manikandan, 2011). For this assignment, the standard deviation that was calculated from the provided data set was 29, while the interquartile, difference between the 1st and 3rd quartile, is determined to be 46.5. There appears to be a significant difference between these two numbers, as the interquartile range is nearly twice that of the standard deviation. Despite this, a significant amount of medical research suggests that standard deviation is the best measure of dispersion, which is why standard deviation is seen as the most commonly used method of measuring dispersion (Ahmed, et al., 2013)
Interpretation of Findings
The first calculation that was conducted on the provided data set involved determining the sample mean. The sample mean refers to the average of a data set that is drawn from a sample of the entire population rather than data drawn from the whole population (Sullivan, 2007). In this case, the sample mean was found to be 196, which indicates that the average cholesterol level among the 9 participants in the sample group is 196.
Sample Standard Deviation
The second calculation made on the data set was that of the sample standard deviation. The sample standard deviation refers to the width of distribution among the various values in the data set as they spread from the mean (Sullivan, 2007). Based on the data set provided, the sample standard deviation was calculated as 29. Ultimately a low sample standard deviation indicates that the values within the data set are all relatively close to the mean, while a higher sample standard deviation is indicative of values that are more spread out from the mean. A sample standard deviation of 29 would certainly be considered high if the data set where comprised of low numbers, such as 11, 13, 39 and 50. Due to the fact that the data set from this case is comprised of rather high numbers, ranging from 175 to 240, a sample standard deviation of 29 may not represent a significant distribution of data in relation to the mean.
The median of a data set refers to the middle number found in that data set when all the values within the data set have been arranged in order from smallest to largest (Sullivan, 2007). The accuracy of the median value can vary from data set to data set. Specifically, data sets that represent values that are tightly grouped and evenly disbursed will lead to a median value that is very close or equal to the mean (average). If, however, there is a significantly high standard deviation, where several of the values within the data set are substantially larger or smaller than the rest of the data, the median may become less accurate. In this case, the median was found to be 194. When compared to the calculated sample mean of 196, it appears that the median is fairly accurate as it is quite close to this sample mean. In addition, this calculation helps to bolster the assessment that the sample standard deviation of 29 that was calculated for this data set is not highly significant.
First and Third Quartile
The first quartile essentially reflects the mean of the lower half of the data set, where 25% of the values within the data set will fall below the first quartile and 75% of the values within the data set will fall above the first quartile (Sullivan, 2007). In contrast, the third quartile reflects the mean of the upper half of the data set, where 75% of the values within the data set will fall below the third quartile and 25% of the values within the data set will fall above the third quartile (Sullivan, 2007). Results from the data set provided revealed that the first quartile was 177.5, while the third quartile was 224. These numbers essentially represent values that are midway between the bottom limit and the mean, as well as the top limit and the mean of the data set.
- Ahmed, H. M., Blaha, M. J., Nasir, K., Jones, S. R., Rivera, J. J., Agatston, A., . . . Blumenthal, R. (2013). Low-risk lifestyle, coronary calcium, cardiovascular events, and mortality: Results from MESA. American Journal of Epidemiology, 178(6), 292-299.
- Insull Jr., W., Toth, P., Mullican, W., Hunninghake, D., Burke, S., Donavan, J. M., & Davidson, M. H. (2001, October). Effectiveness of colesevelam hydrochloride in decreasing LDL cholesterol in patients with primary hypercholesterolemia: A 24-week randomized controlled trial. Mayo Clinic Proceedings, 76(10), pp. 971-982.
- Manikandan, S. (2011). Measure of dispersion. Journal of Pharmacology & Pharmacotherapeutics, 2(4), 315-316.
- Sullivan, L. (2007). Essentials of biostatistics in public health (1st ed.). Burlington, MA: Jones & Bartlett Learning.