gen-define-the-histogram-and-give-one-short-worked-example-8a9b

Define the histogram and give one short worked example.

# Histogram ## Definition A **histogram** is a graphical representation of the distribution of numerical data using adjacent bars (rectangles). The horizontal axis represents intervals (called bins or classes) of data values, and the vertical axis represents the frequency (count) or relative frequency of observations falling within each interval. **Key features:** - Bars touch each other (no gaps for continuous data) - Bar width represents the class interval - Bar height represents frequency - Used for continuous or grouped numerical data --- ## Worked Example **Problem:** The test scores (out of 10) for 20 students are: 5, 6, 7, 3, 8, 7, 9, 6, 5, 7, 8, 4, 6, 7, 8, 9, 5, 6, 7, 8 Create a histogram with class intervals of width 2. **Solution:** **Step 1:** Create frequency table | Class Interval | Tally | Frequency | |---------------|-------|-----------| | 3-4 | II | 2 | | 5-6 | IIII III | 8 | | 7-8 | IIII IIII | 9 | | 9-10 | I | 1 | **Step 2:** Draw the histogram ``` Frequency 10| 9| ┌───┐ 8| │ │ 7| │ │ 6| │ │ 5| │ │ 4| ┌───┐ │ │ 3| │ │ │ │ 2| │ │ │ │ 1|┌─┤ │ │ │┌──┐ 0└─┴───┴─┴───┴┴──┴── 3-4 5-6 7-8 9-10 Score ``` **Interpretation:** Most students scored between 7-8, showing the data is concentrated in the higher range.