Moderate Level Worksheet Questions

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. Number of times a value occursTotal number of valuesRange of valuesAverage of values

Awesome! Frequency is the number of times a particular value appears in a data set.

2. What is a tally mark? Counting marks in groups of 5Drawing marks randomlyMathematical symbolsGraph plotting points

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. 25203050

Perfect! Class mark = (20 + 30) ÷ 2 = 25.

4. Which graph is drawn using bars of equal width and equal spacing between them? HistogramBar graphLine graphPie chart

Excellent! A histogram uses bars of equal width with no gaps between them.

5. What is the difference between class limit and class boundary? Boundaries include gaps between classesNo differenceLimits are always largerBoundaries are whole numbers

Super! Class boundaries fill the gaps between consecutive class intervals.

6. Write the lower limit of the class interval 45–55. 45555010

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? Running total of frequenciesSingle frequency valueMaximum frequencyAverage frequency

Well done! Cumulative frequency is the running sum of all frequencies up to that point.

8. Name two types of bar graphs. SimpleComplexMultipleScattered and multiplecompoundcomplexscattered

Brilliant! Simple and multiple bar graphs are the main types.

9. Define histogram. Graph with bars showing frequency distributionCircular graphLine connecting pointsTable of values

You nailed it! A histogram displays frequency distribution using adjacent bars.

10. State one advantage of using a frequency distribution table. Organizes data clearlyMakes data complexHides patternsIncreases data size

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 5,8,85,8,94,5,8 = frequency =

10–14: Values are 10,12,1210,11,1210,11,13 = frequency =

15–19: Values are 15,15,1815,16,1815,15,19 = frequency =

20–24: Values are 2020,2120,22 → frequency =

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 = Lowerlimit+Upperlimit2upperlimit+lowerlimit2

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: 10, 10, 12, 12, 1210, 11, 12, 12, 1210, 10, 12, 13, 12 where frequency =

15–19: 15, 15, 16, 18, 18, 1815, 16, 16, 18, 18, 1815, 15, 16, 17, 18, 18 → frequency =

20–24: 20, 20, 20, 2220, 20, 21, 2220, 20, 20, 21 → frequency =

25–29: 25, 25, 2825, 26, 2825, 25, 27 → frequency =

30–34: → frequency =

35–39: → frequency =

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:

Step 1: Calculate cumulative frequencies

Cumulative frequency = running total of frequenciesThe highest frequency in the tableThe difference of frequencies

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:

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:

Step 1: Calculate totals

Total students =

Step 2: Find mode

Highest frequency =

Modal class = (class with highest frequency)

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:

Step 1: Calculate total

Total students =

Step 2: Find modal class

Highest frequency =

Most students spend hours on sports

Step 3: Calculate range

Range = Maximum value - Minimum valueMinimum value - Maximum value =

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.

🎉 Outstanding! You've Mastered Frequency Distribution and Data Representation!

Here's what you accomplished:

• Understanding frequency, tally marks, and class intervals

• Creating and interpreting frequency distribution tables

• Calculating class marks, cumulative frequencies, and modal classes

• Organizing raw data into meaningful intervals

• Understanding histogram properties and construction

• Analyzing data patterns using statistical measures

• Converting between different data representation methods

Your solid foundation in data organization and analysis will help you excel in statistics and data science!