Organize raw data into frequency distributions and represent it visually using histograms and frequency polygons.
A frequency distribution table organizes raw data into class intervals, showing how many data points (frequency) fall into each interval.
Marks of 10 students: 45,52,38,60,45,52,45,38,60,52. Find the frequency of 45.
45 appears 3 times, so frequency=3
Why are class intervals used instead of listing every individual value?
Class intervals group data into manageable ranges, making large data sets easier to summarize and visualize
Marks of 8 students: 55,60,55,70,60,55,70,60. Find the frequency of 60.
60 appears 3 times, so frequency=3
A histogram represents frequency distribution with adjacent bars (no gaps) whose heights show frequency. A frequency polygon connects the midpoints of histogram bar tops.
Why are there no gaps between bars in a histogram, unlike a bar graph?
Because histograms represent continuous data (class intervals), where the classes are adjacent without gaps
How is a frequency polygon typically drawn from a histogram?
By joining the midpoints of the tops of each bar with straight lines, sometimes extended to the x-axis at both ends
Why can a frequency polygon be extended to touch the x-axis at both ends?
To show the frequency dropping to zero just outside the range of the actual data, making the enclosed area meaningful for comparison
1. Data: 12,15,12,18,15,12,20. Find the frequency of 12.
2. Data: 5,7,5,9,7,5,9,9. Find the mode (most frequent value) and its frequency.
3. Why is a histogram suited for continuous data rather than categorical data?
4. A class interval is 10-20 with frequency 8. What does this tell us?
5. What is the key difference between a histogram and a frequency polygon?
6. Data: 14,18,14,22,18,14. Find the frequency of 14.
7. Data: 7,9,7,11,9,7,11. Find the mode.
8. Why is a histogram unsuitable for categorical (non-numeric) data?
9. A class interval is 20-30 with frequency 12. What does this tell us?
10. What is plotted on the y-axis of a frequency polygon?