Histograms (Varying Base Lengths) MCQs Quiz | Class 9
Test your understanding of Class IX Mathematics (Code 041) Unit VI: Statistics with this quiz on Histograms (Varying Base Lengths). This study module covers Construction and the frequency density concept. Complete the questions below, submit to check your score, and download the full solution PDF for your exam preparation.
Understanding Histograms with Varying Base Lengths
In Class 9 Statistics, we often encounter grouped frequency distributions where the class intervals are not of equal width. When drawing a histogram for such data, simply plotting the frequency on the vertical axis gives an incorrect representation because the area of the rectangle would not be proportional to the frequency. To correct this, we use the concept of Frequency Density or Adjusted Frequency.
Key Concepts
- Proportional Area: In a histogram, the area of each rectangle represents the frequency. If widths vary, heights must be adjusted.
- Minimum Class Size: We usually select the smallest class width from the data as the standard unit.
- Adjusted Frequency Formula:
Adjusted Frequency = (Frequency of the class / Width of the class) x Minimum Class Width - Vertical Axis: When widths vary, the Y-axis represents “Frequency Density” or “Adjusted Frequency,” not the raw frequency.
Example Calculation
Consider a dataset where the minimum class width is 10.
| Class Interval | Width | Frequency | Calculation | Height (Adj. Freq) |
|---|---|---|---|---|
| 10-20 | 10 | 5 | (5 / 10) x 10 | 5 |
| 20-40 | 20 | 12 | (12 / 20) x 10 | 6 |
Quick Revision Points
- Identify the class with the minimum width (denoted as ‘h’).
- Calculate the width of every other class interval.
- Apply the formula to find the new height for each rectangle.
- Draw the histogram with class intervals on the X-axis and Adjusted Frequency on the Y-axis.
Extra Practice Questions
1. Why is the area of the rectangle important in a histogram?
2. If the minimum class size is 5 and a class has width 15 and frequency 30, what is the length of the rectangle?
3. Does the X-axis scale change when using varying base lengths?
4. Can a histogram have gaps between bars if the intervals are continuous?
5. Define Frequency Density.
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