CBSE Class 6 Mathematics Data Handling Worksheet Set 07

CHAPTER: DATA HANDLING

Question 1. A collection of numbers gathered to get some information is called:
(a) Range
(b) Data
(c) Frequency
(d) None of the options
Answer: (b) Data
Data is a collection of numbers or facts gathered to give some specific information.
In simple words: Data refers to collected facts or numbers.

Exam Tip: Remember the basic definitions of statistical terms like data, range, and frequency.

Question 2. Number of times a particular value in data occurs is called its:
(a) Range
(b) Data
(c) Frequency
(d) None of the options
Answer: (c) Frequency
Frequency tells us how many times a particular observation appears in the given data.
In simple words: Frequency is the count of how often a value occurs.

Exam Tip: Frequency counts repetitions in a dataset.

Question 3. The difference of maximum and minimum value in data is called:
(a) Range
(b) Data
(c) Frequency
(d) None of the options
Answer: (a) Range
Range = Maximum value - Minimum value.
In simple words: Range measures the spread from the lowest to the highest value.

Question 4. Pictorial representation of data is called:
(a) Bar Graph
(b) Histogram
(c) Pictograph
(d) None of the options
Answer: (c) Pictograph
A pictograph represents data using symbols, pictures, or icons.
In simple words: A pictograph uses pictures to show data.

Exam Tip: 'Picto' refers to pictures, which distinguishes it from bar graphs that use bars.

Question 5. The marks obtained by 25 students in a class test of 100 marks are as follows:
80, 60, 40, 70, 75, 80, 90, 100, 60, 70, 60, 70, 85, 65, 70, 70, 85, 60, 65, 80, 60, 70, 80, 70, 60.
Make a frequency distribution of the above data and answer the following questions:
Answer:
First, let us organize the data using tally marks in a frequency distribution table:

In simple words: We count each mark occurrence and group them into a table.

Exam Tip: Always cross-check the sum of frequencies with the total number of items given in the question (25 students).

Question 5(i). What is the maximum marks obtained?
Answer: 100
In simple words: The highest number in the dataset is 100.

Exam Tip: Scan the data for the largest numerical value.

Question 5(ii). Find the number of students who scored less than 75 marks.
Answer:
Students scoring less than 75 marks include those who scored 40, 60, 65, and 70 marks.
Number of students = 1 (for 40) + 7 (for 60) + 2 (for 65) + 7 (for 70) = 17
In simple words: Add up the frequencies of all marks strictly below 75.

Exam Tip: "Less than 75" means 75 is excluded.

Question 5(iii). Find the number of students who scored more than 80 marks.
Answer:
Students scoring more than 80 marks include those who scored 85, 90, and 100 marks.
Number of students = 2 (for 85) + 1 (for 90) + 1 (for 100) = 4
In simple words: Count students with marks 85, 90, and 100.

Exam Tip: "More than 80" means 80 is excluded.

Question 5(iv). Find the range of the data given.
Answer:
Maximum value = 100
Minimum value = 40
Range = Maximum value - Minimum value = 100 - 40 = 60
In simple words: Subtract the lowest score from the highest score.

Exam Tip: Range = Highest - Lowest.

Question 6. Read the pictograph given below and answer the following questions (sales of fan on different days of a week):
Monday: [Star] [Star] [Star] [Star]
Tuesday: [Star] [Star] [Star] [Star] [Star]
Wednesday: [Star] [Star] [Star]
Thursday: [Star] [Star] [Star]
Friday: [Star] [Star]
Saturday: [Star] [Star] [Star] [Star]
Sunday: [Star] [Star] [Star]
Each [Star] represents 10 fans.
Answer:
Let us first calculate the sales for each day:
- Monday: 4 \times 10 = 40 fans
- Tuesday: 5 \times 10 = 50 fans
- Wednesday: 3 \times 10 = 30 fans
- Thursday: 3 \times 10 = 30 fans
- Friday: 2 \times 10 = 20 fans
- Saturday: 4 \times 10 = 40 fans
- Sunday: 3 \times 10 = 30 fans
In simple words: Multiply the number of star symbols by 10 for each day.

Exam Tip: Always note the key value assigned to each symbol before solving.

Question 6(a). How many fans were sold on Monday?
Answer: 40 fans
In simple words: Monday has 4 stars, so 4 \times 10 = 40 fans.

Question 6(b). On which day the maximum number of fans were sold?
Answer: Tuesday (50 fans)
In simple words: Tuesday has the highest number of star symbols (5 stars).

Exam Tip: Look for the row with the maximum number of icons.

Question 6(c). On which day the minimum number of fans were sold?
Answer: Friday (20 fans)
In simple words: Friday has the fewest star symbols (2 stars).

Exam Tip: Look for the row with the fewest icons.

Question 6(d). Find the total number of fans sold during the week.
Answer:
Total fans = 40 (Mon) + 50 (Tue) + 30 (Wed) + 30 (Thu) + 20 (Fri) + 40 (Sat) + 30 (Sun) = 240 fans
In simple words: Add the sales of all 7 days together.

Exam Tip: Alternatively, count the total number of stars across all days (24 stars) and multiply by 10 to get 240.

Question 7. The following table shows the monthly expenditure by Charu's family on various items:
[Table: House Rent: Rs. 5000, Food: Rs. 3500, Education: Rs. 6000, Electricity: Rs. 2500, Transport: Rs. 3000, Miscellaneous: Rs. 4000]
Represent the given data in the form of a bar graph. Choose the scale [Square] as 500 units.
Answer:
Scale: 1 unit length = 500 units (Rs. 500)
Height of bars in units:
- House Rent = \(\frac{5000}{500} = 10\) units
- Food = \(\frac{3500}{500} = 7\) units
- Education = \(\frac{6000}{500} = 12\) units
- Electricity = \(\frac{2500}{500} = 5\) units
- Transport = \(\frac{3000}{500} = 6\) units
- Miscellaneous = \(\frac{4000}{500} = 8\) units
In simple words: Divide each expenditure by 500 to find the bar heights on the graph.

Exam Tip: Clearly mention the chosen scale on the graph sheet.

Question 8. Following table shows the number of trees planted from the months of April to November 2013:
[Table: April: 3000, May: 2000, June: 5000, July: 7000, August: 8000, September: 4000, October: 6000, November: 7000]
Express the data given in the form of a bar graph taking 1 unit length as 1000 plants.
Answer:
Scale: 1 unit length = 1000 plants
Height of bars in units:
- April = 3 units
- May = 2 units
- June = 5 units
- July = 7 units
- August = 8 units
- September = 4 units
- October = 6 units
- November = 7 units
In simple words: Divide the number of trees by 1000 to determine bar heights.

Exam Tip: Maintain equal spacing between all bars in a bar graph.

Question 9. The data given below shows the average rainfall in Cherrapunji, from June to November of a certain year:
[Table: June: 30, July: 35, August: 25, September: 20, October: 15, November: 15]
Draw a bar graph to represent this information.
Answer:
Scale: Let 1 unit length = 5 cm of rainfall
Height of bars in units:
- June = \(\frac{30}{5} = 6\) units
- July = \(\frac{35}{5} = 7\) units
- August = \(\frac{25}{5} = 5\) units
- September = \(\frac{20}{5} = 4\) units
- October = \(\frac{15}{5} = 3\) units
- November = \(\frac{15}{5} = 3\) units
In simple words: Draw bars corresponding to each month's rainfall value.

Exam Tip: Label axes properly with units (Rainfall in cm, Months).

Question 10. The bar graph given below shows the amount of wheat purchased by the government in the year 2000-2004.
Read the bar graph and write down your observations:
Answer:
Based on the provided bar graph:
- 2000: 15 thousand tonnes
- 2001: 25 thousand tonnes
- 2002: 20 thousand tonnes
- 2003: 20 thousand tonnes
- 2004: 30 thousand tonnes
In simple words: Read the height of each bar against the vertical axis.

Exam Tip: Pay attention to the scale indicated on the vertical axis (thousand tonnes).

Question 10(i). In which year was the wheat production maximum?
Answer: 2004 (30 thousand tonnes)
In simple words: The tallest bar is in the year 2004.

Exam Tip: Identify the highest bar on the graph.

Question 10(ii). In which year was the wheat production minimum?
Answer: 2000 (15 thousand tonnes)
In simple words: The shortest bar is in the year 2000.

Exam Tip: Identify the lowest bar on the graph.

Question 10(iii). In which two years the wheat production was same?
Answer: 2002 and 2003 (both have 20 thousand tonnes)
In simple words: The bars for 2002 and 2003 have the exact same height.

Question 10(iv). How many tonnes of wheat production in 2004 was more than wheat production in 2000?
Answer:
Production in 2004 = 30 thousand tonnes
Production in 2000 = 15 thousand tonnes
Difference = 30 - 15 = 15 thousand tonnes (or 15,000 tonnes)
In simple words: Subtract the production of 2000 from 2004.

Exam Tip: Difference questions require subtraction between two specific values.