Shortcomings Of Central Tendency

Sample Solution

Mean

The mean is the most common measure of central tendency. It is calculated by adding up the values of all observations and dividing by the number of observations.

One shortcoming of the mean is that it is susceptible to outliers. Outliers are values that are significantly higher or lower than the rest of the data. Outliers can skew the mean, making it difficult to get an accurate picture of the central tendency of the data.

Full Answer Section

Another shortcoming of the mean is that it is not a good measure of central tendency for data that is not normally distributed. A normal distribution is a bell-shaped curve where the majority of the data points are clustered around the mean. If the data is not normally distributed, the mean may not be representative of the central tendency of the data.

Median

The median is the middle value in a set of data that has been ordered from least to greatest. If there are two middle values, the median is the average of those two values.

One shortcoming of the median is that it does not use all of the data in the set. Instead, it only uses the middle value(s). This can be a problem if the data is skewed or if there are outliers.

Another shortcoming of the median is that it is not as precise as the mean. This is because the median does not use all of the data in the set.

Mode

The mode is the most frequent value in a set of data.

One shortcoming of the mode is that it is not a good measure of central tendency if there are multiple modes or if there is no mode.

Another shortcoming of the mode is that it is not a good measure of central tendency for data that is not normally distributed. If the data is not normally distributed, the mode may not be representative of the central tendency of the data.

Example of the use of a measure of central tendency by the media

In 2016, the New York Times published an article titled "Average American Household Income Reaches Record High." The article reported that the median household income in the United States had reached a record high of $53,709 in 2015.

The article also reported that the mean household income was $56,516 in 2015. However, the article did not mention that the mean household income was skewed by a small number of very high-income households.

If the New York Times had used the median instead of the mean, the article would have presented a more accurate picture of the central tendency of household income in the United States.

Evaluation of the use of a measure of central tendency by the media

The New York Times' use of the mean household income in the article is misleading. The mean household income is skewed by a small number of very high-income households. This means that the mean household income is not representative of the central tendency of household income in the United States.

The New York Times should have used the median household income instead of the mean household income. The median household income is not skewed by outliers, so it is a more accurate measure of the central tendency of household income in the United States.

Recommendation for a better measure

The median household income is a better measure of central tendency than the mean household income because it is not skewed by outliers. The median household income is also a better measure of central tendency for data that is not normally distributed.

Conclusion

The mean, median, and mode are all useful measures of central tendency. However, each of these measures has its own shortcomings. It is important to choose the right measure of central tendency for the data you are using.

If you are unsure which measure of central tendency to use, it is always a good idea to consult with a statistician.