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.
Data handling involves collecting, organizing, analyzing, and interpreting numerical information using statistical measures. Mastering concepts like mean, median, mode, range, frequency distributions, and graphical representations is essential for data analysis in science, business, and research.
Let's explore fundamental concepts of data handling and statistical measures.
1. Define range of a data set.
Perfect! Range measures the spread of data by finding the difference between maximum and minimum values.
2. The runs scored in 5 matches are 45, 60, 35, 80, 70. Find the range.
Step 1: Highest value =
Step 2: Lowest value =
Step 3: Range = 80 - 35 =
Excellent! Range = Maximum - Minimum = 80 - 35 = 45.
3. What is the median of 12, 18, 10, 15, 20?
Step 1: Arrange in order:
Step 2: Middle value (3rd position) =
Great! For odd number of values, median is the middle value after arranging in order.
4. Which measure of central tendency is most affected by extreme values?
Correct! Mean is most sensitive to outliers because it uses all values in calculation.
5. Find the mode of 5, 7, 5, 9, 5, 7, 6, 5.
Step 1: Count frequencies: 5 appears
Step 2: Mode (most frequent) =
Perfect! Mode is the value that appears most frequently in the dataset.
6. In a histogram, what does the area of each rectangle represent?
Correct! In histograms, the area of each bar represents the frequency of that class.
7. Daily temperatures: 30°C, 32°C, 29°C, 35°C, 31°C, 28°C, 30°C. Find the mean temperature.
Step 1: Sum = 30+32+29+35+31+28+30 =
Step 2: Mean = 215 ÷ 7 =
Excellent! Mean = Sum of observations ÷ Number of observations.
8. What type of bar graph is used to compare two related sets of data?
Perfect! Double bar graphs allow side-by-side comparison of two datasets.
9. If the mean of 8 numbers is 15, what is their sum?
Step 1: Mean =
Step 2: Sum =
Great! Using the relationship: Sum = Mean × Count.
Drag each concept to its correct category:
Part B: Short Answer Questions (2 Marks Each)
1. Marks of 10 students: 15, 20, 25, 15, 30, 20, 25, 15, 20, 30. Prepare frequency table.
Step 1: Count each value
Mark 15 appears:
Mark 20 appears:
Mark 25 appears:
Mark 30 appears:
Perfect! Frequency table shows how often each value appears.
2. Weights of 8 children: 35, 40, 38, 35, 42, 40, 38, 35. Find the mode.
Step 1: Count frequencies
35 kg appears
Step 2: Identify most frequent
Most frequent weight =
Excellent! 35 kg is the mode as it appears most frequently.
3. Find median of: 12, 18, 14, 20, 16, 18, 14, 20.
Step 1: Arrange in ascending order
Ordered data: 12, 14, 14, 16, 18, 18, 20, 20
Step 2: Find middle values (4th and 5th positions)
Middle values: 16 and 18
Step 3: Calculate median
Median = (16 + 18) ÷ 2 =
Great! For even number of values, median is average of two middle values.
4. Heights of 5 boys: 150, 155, 160, 165, 170 cm. Find range and mean.
Step 1: Calculate range
Range = Highest - Lowest = 170 - 150 =
Step 2: Calculate mean
Sum = 150+155+160+165+170 = 800
Mean = 800 ÷ 5 =
Perfect! Range measures spread, mean measures central tendency.
Part C: Long Answer Questions (4 Marks Each)
1. Marks of 30 students: 12, 15, 18, 20, 22, 15, 14, 18, 19, 20, 18, 17, 15, 14, 16, 19, 20, 21, 18, 15, 14, 16, 17, 18, 19, 15, 20, 21, 18, 17.
Step 1: Create frequency table
Count frequency of each mark:
Frequency of 15 =
Frequency of 18 =
Frequency of 20 =
Step 2: Calculate sum and mean
Sum of all marks =
Mean marks = 510 ÷ 30 =
Excellent! Systematic counting and calculation of mean from large dataset.
2. Heights: 140, 145, 150, 155, 150, 160, 145, 150, 155, 150, 145, 160, 155, 150, 145.
Step 1: Find frequencies
Count each height value:
Frequency of 150 cm =
Step 2: Identify mode
Mode =
Step 3: Find median
With 15 values, median =
Outstanding! Mode and median are both 150 cm for this dataset.
3. Daily wages: ₹100, ₹120, ₹140, ₹160, ₹180, ₹200, ₹220, ₹240, ₹260, ₹280. Group with class size 40.
Step 1: Create class intervals
Classes: 100-140, 140-180, 180-220, 220-260, 260-300
Step 2: Count frequencies
Class 100-140: frequency =
Class 140-180: frequency =
Class 180-220: frequency =
Class 220-260: frequency =
Class 260-300: frequency =
Perfect! Grouped frequency distribution organizes data into meaningful intervals.
4. Electricity consumption: 120, 150, 130, 140, 110, 125, 135, 145, 155, 160, 150, 140, 130, 135, 145.
Step 1: Group into ranges
Range 110-120: frequency =
Range 120-130: frequency =
Range 130-140: frequency =
Range 140-150: frequency =
Range 150-160: frequency =
Step 2: Calculate overall statistics
Sum = 2055, Mean consumption = 2055 ÷ 15 =
Excellent! Comprehensive analysis of electricity consumption data.
Test your understanding with these multiple choice questions:
For each question, click on the correct answer:
1. The mean of 10, 20, 30 is:
(a) 20 (b) 25 (c) 30 (d) 15
Correct! Mean = (10 + 20 + 30) ÷ 3 = 60 ÷ 3 = 20.
2. The range of 25, 35, 45, 40 is:
(a) 20 (b) 10 (c) 15 (d) 25
Correct! Range = Maximum - Minimum = 45 - 25 = 20.
3. In a bar graph, the height of the bar shows:
(a) Frequency (b) Class interval (c) Mean (d) Median
Correct! In bar graphs, the height represents the frequency of each category.
4. The mode of 4, 4, 5, 5, 5, 6, 7 is:
(a) 4 (b) 5 (c) 6 (d) 7
Correct! Mode is 5 because it appears most frequently (3 times).
5. Which of the following is not a measure of central tendency?
(a) Mean (b) Median (c) Mode (d) Range
Correct! Range measures spread (dispersion), not central tendency.
🎉 Outstanding! You've Mastered Hard Level Data Handling! Here's what you accomplished:
✓ Statistical Measures Mastery: Mean, median, mode, and range calculations
✓ Frequency Distribution: Creating and interpreting frequency tables
✓ Data Organization: Grouping data into classes and intervals
✓ Graphical Representation: Bar graphs, histograms, double bar graphs
✓ Central Tendency Analysis: Understanding when to use different measures
✓ Large Dataset Handling: Processing 30+ data points systematically
✓ Real-World Applications: Analyzing wages, consumption, academic performance
✓ Data Interpretation: Drawing meaningful conclusions from statistical analysis
Your expertise in data handling prepares you for advanced statistics, research methodology, data science, and evidence-based decision making!