When a histogram is too wide or too narrow, it becomes less useful for understanding the data.
Both histograms and curves are types of distributionsβthey show us the probability of measurements.
- Collecting data and plotting it on a graph gives us a histogram.
- Extracting insights from that graph gives us a distribution.
Example:
Imagine we collect the heights of all our classmates and plot them on a graph. That graph is the histogram.
Then, we analyze that graph to find insights, such as:
- What is the tallest height?
- What is the shortest height?
- What is the average height?
- Which height does no one have?
- What is the probability of a classmate being exactly 5 feet tall?
Finding these answers and understanding the overall pattern of the data is what we call the distribution.
Normal Distribution
The Gaussian distribution, also known as the Normal Distribution, is shaped like a bell.
This bell shape occurs because most data points are clustered around the average, while only a few are much higher or lower. As a result, the middle of the graph is tall, and the two sides taper offβjust like a bell.
- If the data is tightly centered around the average, the bell becomes narrow. This indicates low variance.
- If the data is spread out far from the average, the bell becomes wide. This indicates high variance.
Central Limit Theorem
If the histogram is not bell-shaped, we can take samples from different groups.
Then, we calculate the average of each group and create a new histogram using those averages.
By doing this, the resulting histogram will tend to form a bell-shaped curve.
This is known as the Central Limit Theorem.
- Population: When the number of participants equals the total number of individuals we are studying, we refer to them as the population, and their characteristics are called population parameters.
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