When to use median vs. mean

Definition

The decision to use median or mean as a measure of central tendency depends on the nature of the data and its distribution. The median is the middle value that separates the higher half from the lower half of a data set, making it less sensitive to outliers, while the mean is the arithmetic average that can be skewed by extreme values. Understanding when to use each measure is crucial for accurately interpreting data in various contexts.

5 Must Know Facts For Your Next Test

1. The median is preferred when dealing with skewed distributions or datasets with outliers, as it provides a more accurate reflection of central tendency.
2. The mean is suitable for normally distributed data where all values are fairly representative and there are no extreme outliers affecting the calculation.
3. In income data, which often has a right skew (a few high earners), the median can provide a better picture of the typical income than the mean.
4. When analyzing ordinal data (data that can be ranked but not measured), using the median is more appropriate than using the mean.
5. In larger datasets, even a few outliers can significantly affect the mean, making it essential to analyze data distribution before deciding on which measure to use.

Review Questions

• How does the presence of outliers influence your choice between using median and mean?
  • Outliers can significantly skew the mean, making it an unreliable measure of central tendency in such cases. For instance, if there are extremely high or low values in a dataset, they can pull the mean away from the center of most values. In contrast, the median remains unaffected by outliers, as it simply represents the middle value. Therefore, when outliers are present, it's generally better to use the median to get a true sense of central tendency.
• Discuss how skewness in data distribution affects whether to use median or mean.
  • Skewness in data distribution plays a critical role in choosing between median and mean. If a dataset is positively skewed (with a long right tail), the mean will be greater than the median due to higher values pulling it up. Conversely, if the data is negatively skewed (with a long left tail), the mean will be less than the median. In both cases, using the median provides a more accurate representation of central tendency because it isn't influenced by extreme values.
• Evaluate a scenario where choosing between median and mean would impact decision-making based on data analysis.
  • Consider a real estate market analysis where you are looking at home prices in an area. If most homes are priced around $300,000 but there are a few luxury homes priced at $1 million, using the mean could suggest an average price that doesn't reflect what most buyers would pay. This could lead investors or potential buyers to overestimate property values. Instead, using the median would give a clearer picture of typical home prices in that market, aiding better investment decisions and understanding of affordability for buyers.

Related terms

Outlier: An outlier is a data point that differs significantly from other observations in a dataset, which can distort statistical measures like the mean.

Skewness: Skewness refers to the asymmetry in the distribution of data, which affects whether the mean or median is a better representation of central tendency.

Data Distribution: Data distribution describes how values are spread across a dataset and influences the choice between using mean or median to summarize data.