Hard Level Worksheet Questions
Interactive Frequency Distribution Tables and Graphs Worksheet
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
Frequency distribution tables and graphs are powerful tools for organizing, analyzing, and presenting statistical data. Understanding histograms, bar graphs, pie charts, and frequency polygons is essential for data interpretation and statistical analysis in real-world applications.
Let's start with fundamental concepts of frequency distribution and data representation.
1. Define "frequency" in a frequency distribution table.
Perfect! Frequency is the number of times a particular value or data item appears in a dataset.
2. What is the class mark of the class interval 20–30?
Class mark =
Excellent! Class mark is the mid-point of the class interval: (20+30)/2 = 25.
3. The sum of all frequencies in a frequency table is called what?
Correct! The total frequency is the sum of all individual frequencies in the table.
4. Which type of graph is most suitable for representing parts of a whole?
Perfect! Pie charts show how different parts make up a complete whole using sectors of a circle.
5. If the class interval is 40–50, find its class size.
Step 1: Class size = Upper limit - Lower limit
Step 2: Class size = 50 - 40 =
Great! Class size is the difference between upper and lower limits.
6. The mid-value between 15 and 25 is called the:
Correct! The mid-value or midpoint of a class interval is called the class mark.
7. State the difference between a bar graph and a histogram.
Excellent! Bar graphs have gaps between bars, while histogram bars touch each other.
8. If the highest frequency in a table is 18, what is its class called?
Perfect! The class with the highest frequency is called the modal class.
9. What is the difference between grouped and ungrouped data?
Correct! Grouped data is organized into class intervals, while ungrouped data shows individual values.
10. Which axis is generally used to represent the variable in a histogram?
Great! The X-axis represents the variable (class intervals) in a histogram.
Drag each data representation to its most suitable graph type:
Part B: Short Answer Questions (2 Marks Each)
1. Prepare tally marks for shoe sizes: 5, 6, 5, 7, 8, 6, 5, 9, 8, 7, 6, 5, 6, 7, 5, 9, 8.
Step 1: Count each size
Size 5 appears:
Size 6 appears:
Size 7 appears:
Size 8 appears:
Size 9 appears:
Perfect! Counting frequencies: Size 5→5, Size 6→4, Size 7→3, Size 8→3, Size 9→2.
2. Find class marks for: 0–10, 10–20, 20–30, 30–40.
Step 1: Apply class mark formula
Class mark of 0–10 =
Class mark of 10–20 =
Class mark of 20–30 =
Class mark of 30–40 =
Excellent! Class marks are the midpoints: 5, 15, 25, 35.
3. Marks of 10 students: 8, 7, 6, 9, 7, 8, 10, 6, 9, 7. Prepare frequency table.
Step 1: Count each mark
Mark 6 appears:
Mark 7 appears:
Mark 8 appears:
Mark 9 appears:
Mark 10 appears:
Perfect! Frequency table: 6→2, 7→3, 8→2, 9→2, 10→1.
4. For histogram data 0–10(5), 10–20(8), 20–30(12), 30–40(7), 40–50(3):
Step 1: Identify highest frequency
Highest frequency =
Step 2: Find modal class
Modal class =
Great! The class 20-30 has the highest frequency (12), making it the modal class.
Part C: Long Answer Questions (4 Marks Each)
1. For electricity bills of 40 houses, create grouped frequency table with class size 50 starting from 300–350.
Sample data: 320, 420, 480, 520, 380, 450, 590, 610, 470, 530...
Step 1: Set up class intervals
Class 300–350: frequency =
Class 350–400: frequency =
Class 400–450: frequency =
Class 450–500: frequency =
Class 500–550: frequency =
Class 550–600: frequency =
Class 600–650: frequency =
Class 650–700: frequency =
Excellent! Grouped frequency table shows distribution of electricity bills across different ranges.
2. For frequency polygon construction from given table:
| Class Interval | Frequency |
|---|---|
| 0–10 | 2 |
| 10–20 | 5 |
| 20–30 | 8 |
| 30–40 | 15 |
| 40–50 | 20 |
| 50–60 | 10 |
Step 1: Find class marks
Class marks:
Step 2: Plot points
Step 3: Connect points
Join points with
Step 4: Complete the polygon
Extend to
Perfect! Frequency polygon shows the shape of data distribution.
3. Create pie chart for family budget (Total = ₹22,000) where Rent ₹8000, Food ₹6000, Education ₹4000, Savings ₹2000, Miscellaneous ₹2000
Step 1: Calculate angles
Rent angle = (8000/22000) × 360° =
Food angle = (6000/22000) × 360° =
Education angle = (4000/22000) × 360° =
Savings angle = (2000/22000) × 360° =
Miscellaneous angle = (2000/22000) × 360° =
Step 2: Verify total
Total angles =
Outstanding! Pie chart represents budget allocation proportionally.
4. Bar graph construction for sales data, where sales: Rice ₹5000, Wheat ₹7000, Sugar ₹3000, Pulses ₹4000
Step 1: Set up axes
X-axis: Products, Y-axis: Sales amount
Step 2: Draw bars
Rice bar height:
Wheat bar height:
Sugar bar height:
Step 3: Ensure uniformity
All bars should have
Excellent! Bar graph effectively compares sales across different products.
Test your understanding with these multiple choice questions:
For each question, click on the correct answer:
1. In a histogram, frequencies are represented on:
(a) X-axis (b) Y-axis (c) Both axes (d) None
Correct! In a histogram, the Y-axis represents frequencies while X-axis shows class intervals.
2. The mid-point of 20–30 is:
(a) 20 (b) 25 (c) 30 (d) 15
Correct! Class mark = (20 + 30) ÷ 2 = 25.
3. In a frequency polygon, the frequencies are represented by:
(a) Bars (b) Points joined by lines (c) Circles (d) Rectangles
Correct! Frequency polygon connects class marks with straight lines to show data distribution.
4. The suitable graph to represent monthly expenditure on different heads is:
(a) Histogram (b) Bar Graph (c) Pie Chart (d) Frequency Polygon
Correct! Pie chart is ideal for showing how different parts make up the whole monthly budget.
5. The sum of all sector angles in a pie chart is:
(a) 90° (b) 180° (c) 270° (d) 360°
Correct! A complete circle contains 360°, so all pie chart sectors must sum to 360°.
🎉 Outstanding! You've Mastered Hard Level Frequency Distribution and Graphs! Here's what you accomplished:
✓ Advanced Frequency Concepts: Class marks, modal class, class size, and total frequency
✓ Complex Data Organization: Grouped frequency tables with various class intervals
✓ Histogram Construction: Understanding continuous data representation and bar properties
✓ Bar Graph Mastery: Comparing categorical data with proper scaling and spacing
✓ Pie Chart Calculations: Converting data to angles and proportional representation
✓ Frequency Polygon Construction: Connecting class marks to show data distribution
✓ Tally Mark Systems: Efficient data counting and frequency determination
✓ Graph Selection Skills: Choosing appropriate graphs for different data types
✓ Real-World Applications: Budget analysis, sales data, student performance, demographics
Your expertise in frequency distribution and graphical representation prepares you for advanced statistics, data analysis, and research methodology!