# When is the median preferred over the mean to describe a variable?

In the case of Neighborhood C, you mentioned it had a bimodal dispersion. How might other measures, such as the standard deviation, have provided additional insights into the distribution of house prices within the neighborhood?

Statistics Questions

Question 1: Although the mean is used most often as a measure of central tendency, when might someone prefer mode over mean or median? When is the median preferred over the mean to describe a variable?

The kind of data, the conveyance of the data, and the specific targets of the study will decide whether the mean, median, or mode should be utilized as a measure of central tendency. The mean is usually utilized when analyzing persistent, numerical information such as interval or proportion statistics (Mishra et al., 2019). It may be communicated as the total value divided by the number of data points. Extraordinary values, or exceptions, within the information, might influence the mean. It might not be the ideal alternative if the information contains eminent exceptions or is not frequently dispersed (Kaliyadan & Kulkarni, 2019). For instance, given a dataset of salary levels, the mean may not be as demonstrative of the commonplace person’s wage as it might be if it is altogether affected by a small number of exceptionally high workers.

The median is a dependable indicator of central tendency that is less affected by exceptions. When working with skewed or non-normally disseminated information, or when it is ordinal, it is regularly chosen over the mean (Mishra et al., 2019). When sorting all the information focused in a dataset that contains exceptions, the median demonstrates the middle value. Because a couple of exceptionally high or low values can skew the mean, this makes it a much better choice for factors like family salary (Gravetter et al., 2021). The median is frequently utilized when information is displayed as positions or organized categories.

When working with category or nominal information, the mode is most helpful when values are not on a numerical scale but may fall into discrete categories. In these circumstances, there is no need to utilize the terms mean or median; instead, the mode indicates the category that happens most habitually. For instance, the color most respondents chose in a survey inquiring them to choose their favorite color would appear by the mode (Kaliyadan & Kulkarni, 2019). In discrete numerical data, just like the number of children in a family, the mode may also be utilized to express the foremost ordinary number of children.

Question 2: What are some ways in which measures of central tendency can inadvertently lead to bad decisions?

When utilized in isolation without considering the data distribution, measures of central tendency like the mean and median might result in destitute conclusions. The mean property cost in each community appeared to be the fitting choice for decision-making in the canvassing for donations (Gravetter et al., 2021). But when there are extraordinary exceptions or an unpredictable information distribution, this procedure may not work as intended. Since Neighborhood C had the highest mean house cost in this instance, it was chosen at first. A more profound look at the information showed that Neighborhood C had a bimodal dispersion with both high- and low-value properties. This data was unclear when the mean was considered (Kaliyadan & Kulkarni, 2019). This emphasizes how significant it is to incorporate components other than the mean when assessing the central tendency since the mean might cloud the nuanced viewpoints of the information.

Furthermore, when considering the median, Neighborhood B—which had the second-highest cruel house price—also turned out to be a terrible choice. The mean was pushed upward by several exceedingly costly properties, making it less representative of the larger part of homes within the region. The typical property value within the community was better represented by the median, which was much lower than the mean (Mishra et al., 2019). The dispersion of the information and the specific necessities or targets of the study ought to be considered when selecting a degree of central tendency; Neighborhood A, on the other hand, had the least mean but the most elevated number of properties esteemed at more than \$100,000. This illustration shows how a single central tendency degree may be misleading and how, to make intelligent judgments, a more careful investigation of the data’s distribution is required (Gravetter et al., 2021).

References

Gravetter, F. J., Wallnau, L. B., Forzano, L. A. B., & Witnauer, J. E. (2021). Essentials of statistics for the behavioral sciences.

Kaliyadan, F., & Kulkarni, V. (2019). Types of variables, descriptive statistics, and sample size. Indian Dermatology Online Journal10(1), 82.

Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of cardiac anesthesia22(1), 67.