The median is one of the three main measures of central tendency, alongside the mean and mode. It represents the middle value of an ordered dataset. It is a powerful and reliable summary statistic and widely used, especially in real-life scenarios where data is skewed or contains outliers. Unlike the mean, the median is not affected by extreme values, which makes it incredibly useful in various fields. For the formula of the median, read the post: formula of median and definition.
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When the Median is Preferred over the Mean
Question: What is a measure of central tendency, and what are the common measures of central tendency? Also, when is the median preferred over the mean?
A measure of central tendency is the single numerical value considered most typical of the values of a quantitative variable.
The most common measure of central tendency is the mode (i.e., the most frequently occurring number)
The median (i.e., the middle point or fiftieth percentile), and the mean (i.e., the arithmetic average).
The median is preferred over the mean when the numbers are highly skewed (i.e., non-normally distributed).
Importance of Measures of Central Tendencies
Since measures of central tendency condense a bunch of information into a single, digestible value that represents the center of the data, this makes measures of central tendencies important for several reasons:
- Summarizing data: Instead of listing every data point, one can use a central tendency measure to get a quick idea of what is typical in the data set.
- Comparisons: By computing central tendency measures for different groups or datasets, one can easily compare them to see if there are any differences.
- Decision making: Central tendency measures can help to make wise decisions. For instance, knowing the average income in an area can help set prices. Imagine an organization is analyzing customer purchases. Knowing the average amount spent can help them tailor promotions or target specific customer groups.
- Identifying trends: Measures of central tendencies may help in observing the trend over time. This can be done by using different visualizations to see if there are any trends, like a rise in average house prices.
However, it is very important to understand these Measures of Central Tendency (mean, median, mode). Each measure of central tendency has its strengths and weaknesses. Choosing the right measure of central tendency depends on the kind of data and what one’s interest is to extract from and try to understand.
Real-Life Examples and Uses of Median
- Income & Salaries: The Median is used to represent the average income of a population more accurately. It is because A few ultra-rich individuals can skew the mean income upward. The median gives a more realistic picture of what a typical person earns. Example: If most people earn around $40,000–$60,000, but a few CEOs earn $10 million or more, the median income might be $55,000 while the mean income could be $95,000 — misleading!
- Education (Test/ Exame Scores): The median can be used to summarize exam results or performance data. A few very low or very high scores can distort the mean. For example, if most students score between 70 and 90, but a few score 10 or 100, the measure of central tendency, the median score, gives a better sense of central performance.
- Real Estate (Home Prices): Reporting the median home price is common in real estate. Why Median? It avoids distortion from a few very expensive or very cheap homes. For example, A city may have a median home price of $350,000, even if some luxury homes cost $5 million.
- Sports (Player Performance): To report median stats like race times, goals scored, or batting averages. To avoid skewed data from one amazing or terrible performance. For example, a runner’s median race time over 10 races can better reflect consistency.
- Healthcare (Medical Test Results): Reporting the median wait time in hospitals or median survival time in clinical trials may be beneficial. This is because medical data often contains outliers or skewed distributions. For example, if most patients wait 30 minutes, but a few wait 5 hours, the measure of central tendency, the median wait time, might be 35 minutes, while the mean could be misleadingly high.
- Customer Feedback (Review Rating): Median star rating for products or services. Filters out extremely negative or overly positive outliers. For example, if ratings are 1, 5, 5, 5, and 1, the mean is 3.4 but the median is 5, better reflecting the typical rating.
- Transportation (Travel Times): Apps like Google Maps or Waze often use median travel times to reflect a more realistic average, ignoring rare traffic jams or super fast times. For example, the median commute time may be 25 minutes, even if a few people experience 60-minute delays.
Summary
| Scenario/ Use Case | Variable | Why Median should be used |
|---|---|---|
| Income reports | Salary | Avoids distortion by billionaires |
| House prices | Real estate values | Neutralizes luxury properties |
| ER performance | Patient wait times | Filters extreme delays |
| Test scores | Exam performance | Reduces skew from outliers |
| Travel times | Commute estimates | Reflects normal travel conditions |
| Product reviews | User ratings | Balances biased reviews |
Read more about measures of Central Tendency
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