Moderate 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 essential tools for organizing and presenting data effectively. Understanding these concepts helps us analyze patterns and draw meaningful conclusions from data.
First, let's explore the basic concepts of frequency distribution and data representation.
1. Define frequency in a data set.
Awesome! Frequency is the number of times a particular value appears in a data set.
2. What is a tally mark?
Great job! Tally marks are counting marks grouped in sets of 5 for easy counting.
3. Write the class mark for the class interval 20–30.
Perfect! Class mark = (20 + 30) ÷ 2 = 25.
4. Which graph is drawn using bars of equal width and equal spacing between them?
Excellent! A histogram uses bars of equal width with no gaps between them.
5. What is the difference between class limit and class boundary?
Super! Class boundaries fill the gaps between consecutive class intervals.
6. Write the lower limit of the class interval 45–55.
That's correct! The lower limit is the smallest value in the class interval.
7. In a frequency table, what does the cumulative frequency represent?
Well done! Cumulative frequency is the running sum of all frequencies up to that point.
8. Name two types of bar graphs.
Brilliant! Simple and multiple bar graphs are the main types.
9. Define histogram.
You nailed it! A histogram displays frequency distribution using adjacent bars.
10. State one advantage of using a frequency distribution table.
Perfect! Frequency tables organize large amounts of data in a clear, understandable format.
Drag each method to its correct category:
Part B: Short Answer Questions (2 Marks Each)
1. Prepare a frequency table for the marks: 5, 12, 8, 15, 18, 12, 10, 20, 8, 15 (Class intervals: 5–9, 10–14, 15–19, 20–24).
Step 1: Count values in each interval
5–9: Values are
10–14: Values are
15–19: Values are
20–24: Values are
Step 2: Verify total
Total frequency =
Excellent! Your frequency table is complete and accurate.
2. Find the class mark for each interval: 0–10, 10–20, 20–30.
We know that the formula for Class mark =
Class mark of 0–10 =
Class mark of 10–20 =
Class mark of 20–30 =
Perfect! Class marks represent the middle value of each interval.
3. From the data, prepare a tally chart: Red: 7, Blue: 5, Green: 8, Yellow: 4.
Step 1: Convert to tally marks (groups of 5)
Step 2: Verify totals
Total items =
Great work! Tally charts make counting and verification easy.
4. Books read data: Class A: 20, Class B: 25, Class C: 15, Class D: 30.
Step 1: Identify extremes
Highest value =
Lowest value =
Class with minimum books =
Class with maximum books =
Excellent analysis! You can easily identify patterns from organized data.
5. Prepare frequency table for marks: 12, 18, 15, 10, 20, 25, 12, 28, 30, 35, 15, 18, 22, 20, 16, 25, 18, 10, 20, 12.
Step 1: Sort and count by intervals
10–14:
15–19:
20–24:
25–29:
30–34:
35–39:
Step 2: Verify total
Total = 5 + 6 + 4 + 3 + 1 + 1 =
Outstanding! Your systematic approach ensures accuracy.
Part C: Long Answer Questions (4 Marks Each)
1. Mathematics test marks of 40 students:
| Marks | Students |
|---|---|
| 0–10 | 4 |
| 10–20 | 6 |
| 20–30 | 10 |
| 30–40 | 8 |
| 40–50 | 6 |
| 50–60 | 6 |
Step 1: Calculate cumulative frequencies
Cumulative frequency =
0–10:
10–20:
20–30:
30–40:
40–50:
50–60:
Step 2: Verify
Last cumulative frequency = Total students =
Perfect! Cumulative frequency shows how many students scored up to each mark range.
2. Weekly wages of 30 workers:
| Wages (₹) | Workers |
|---|---|
| 500–600 | 3 |
| 600–700 | 4 |
| 700–800 | 8 |
| 800–900 | 10 |
| 900–1000 | 5 |
Step 1: Verify total
Total workers =
Step 2: Find modal class
Highest frequency =
Most common wage range =
Step 3: Calculate class mark
Class mark of 700–800 =
Step 4: Histogram property
For histogram, all bars have equal
Excellent analysis! You've identified key statistical measures.
3. Science exam marks:
| Marks | Frequency |
|---|---|
| 0–10 | 2 |
| 10–20 | 6 |
| 20–30 | 7 |
| 30–40 | 5 |
| 40–50 | 4 |
| 50–60 | 6 |
Step 1: Calculate totals
Total students =
Step 2: Find mode
Highest frequency =
Modal class =
Step 3: Calculate cumulative frequency
Up to 10 marks:
Up to 20 marks:
Up to 30 marks:
Great work! You've mastered frequency analysis.
4. Sports hours per week:
| Hours | Students |
|---|---|
| 0–2 | 5 |
| 2–4 | 7 |
| 4–6 | 8 |
| 6–8 | 6 |
| 8–10 | 4 |
Step 1: Calculate total
Total students =
Step 2: Find modal class
Highest frequency =
Most students spend
Step 3: Calculate range
Range =
Step 4: Find minimum frequency
Minimum frequency =
Class interval with minimum frequency =
Outstanding! You've completed a comprehensive data analysis.
Test your understanding with these multiple choice questions:
For each question, click on the correct answer:
1. The middle value of a class interval is called:
(a) Class limit (b) Class mark (c) Class width (d) Class boundary
Super job! Class mark is the middle value: (lower limit + upper limit) ÷ 2.
2. Which diagram is used to represent data continuously?
(a) Bar graph (b) Pie chart (c) Histogram (d) Line graph
Well done! Histograms show continuous data with adjacent bars.
3. In a frequency table, the sum of all frequencies is equal to:
(a) The total number of observations (b) The highest frequency (c) The class interval (d) The range
That's right! Sum of frequencies = total count of all data values.
4. In a histogram, the width of each bar represents:
(a) Class size (b) Frequency (c) Class limit (d) Class boundary
Correct! Bar width shows the class interval size, height shows frequency.
5. The cumulative frequency of the last class is always:
(a) Zero (b) Equal to total observations (c) Equal to class size (d) Maximum frequency
Fantastic! Last cumulative frequency = sum of all frequencies = total observations.