Page 123 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

• Histogram
• A histogram is a bar graph that unveils the distribution of numerical data. Imagine you have a bunch of socks
and want to see how many socks there are of each size. A histogram can help you visualize this for numerical
data! Here’s the breakdown:
• Bins and Counts: The data’s range is divided into sections called bins. You count how many data points fall
within each bin.
• Visualizing with Bars: A bar chart is created where the horizontal axis (x-axis) represents the bin values (like
sock sizes) and the vertical axis (y-axis) represents the frequency (count) of data in each bin. Each bin has a
bar, and the height of the bar reflects how many data points fall within that bin. Here’s what makes histograms
special:
• For Continuous Data: Histograms shine with continuous data, which can take any value within a range (like
heights, weights, or exam scores).
• Revealing Patterns: Unlike pie charts focusing on category proportions, histograms show the shape of your
data’s distribution. You can see if the data clusters around a central value, leans towards one side (skewed),
or has multiple peaks.
• De-cluttering Data: When you have a massive dataset with many data points, histograms are more effective
than bar charts. By grouping values into bins, histograms can handle a large amount of data without becoming
cluttered.
• In essence, histograms are a powerful tool to understand how numerical data spreads out and identify
patterns within your dataset.
• Frequency polygon
• A frequency polygon is a visual representation of data distribution, similar to a histogram but using lines
instead of bars. Here’s a breakdown to understand how it works:
• Data Grouping
• Unlike raw data points, frequency polygons deal with grouped data. This means your data is first divided into
categories or intervals, like height ranges (0-5 ft, 5- 10 ft, etc.).
• Finding Midpoints
• For each data interval (class), we calculate the midpoint. This is essentially the average of the lower and
upper limits of the interval.
• Plotting and Connecting
• The midpoints are plotted on the horizontal axis (x-axis).
• The frequency (number of data points) within each class interval is plotted on the vertical axis (y-axis).
• Finally, these plotted points are connected using straight line segments, forming a polygon-like shape.
• Key Points:
• Highlighting Trends: Frequency polygons excel at showcasing trends in data distribution, especially when
dealing with many class intervals. The line helps visualize how the frequency changes across the data range.
Comparison with Histograms: While both depict data distribution, histograms show the frequency for each
class interval {like bar areas), while frequency polygons focus on the trend between classes (through the
connecting line).
• Use Cases: Frequency polygons are often used for:
Comparing distributions of multiple datasets on the same graph.

Visualizing how data smoothly transitions between categories.
In essence, frequency polygons are a valuable tool for understanding how data is spread across categories and
identifying trends within the data distribution.

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CITS : WCS - Electrical - Exercise 9