Hard Level Worksheet Questions

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:

Monthly budget breakdown

Student marks in different subjects

Height distribution of students

Market share of companies

Sales in different quarters

Age groups in a population

Temperature variation over time

Weight categories of athletes

Pie Chart (Parts of Whole)

Bar Graph (Comparing Categories)

Histogram (Continuous Data)

Line Graph (Time Series)

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: times

Size 6 appears: times

Size 7 appears: times

Size 8 appears: times

Size 9 appears: times

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: times

Mark 7 appears: times

Mark 8 appears: times

Mark 9 appears: times

Mark 10 appears: times

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 = (class with highest frequency)

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 at both ends to close the polygon

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

X-axis

Y-axis

Both axes

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

Bars

Points joined by lines

Circles

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

Histogram

Bar Graph

Pie Chart

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°

90°

180°

270°

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!

Sign in to Innings2

Hard Level Worksheet Questions

Part B: Short Answer Questions (2 Marks Each)

Part C: Long Answer Questions (4 Marks Each)