Measures of Central Tendency
2026-02-28 09:55 Diff
https://brightchamps.com/en-us/math/data/measures-of-central-tendency

When we use mean, median, or mode, the right choice depends on how the data is spread out.
This spread is called a distribution.

Types of Data Distribution

When we look at numbers, they can be arranged in different ways. These arrangements are called distributions. The two common types are:

Normal Distribution: Numbers are spread evenly on both sides. Most values are close to the middle, with only a few very high or very low numbers. For example, if most students score around 70 on a test, only a few might score much higher or lower.

Skewed Distribution: Numbers are not evenly spread. Most values are on one side, while a few are far away on the other.

Right-skewed: Most numbers are small, and only a few are very large.

Left-skewed: Most numbers are significant, and only a few are very small.

Measures of Central Tendency for Normal Distribution

In a normal distribution, most numbers are near the middle, so the mean, median, and mode are usually the same or very close. This makes it easy to find a “typical” value for the data.

Examples of Skewed Distribution

Right-skewed (most low scores, few high scores):

 Marks of 7 students: 40, 45, 50, 55, 60, 90, 95

 Most students scored between 40 and 60, but a few scored very high. In this case, the mean is greater than the median, which is greater than the mode.

Left-skewed (most high scores, few low scores):

 Marks: 40, 80, 85, 90, 92, 95, 98

 Most students scored high, but one scored low. Here, the mean is less than the median, which is less than the mode.

Tip: In skewed distributions, the median is usually a better measure of the middle value because the mean can be affected by extreme values.