Data Handling is the process of collecting, organizing, analyzing, interpreting, and presenting data in a meaningful way. It involves transforming raw data into information that can be easily understood and used for decision-making.
Key Concepts:
- Data Collection: Gathering information from various sources (surveys, observations, experiments).
- Organization: Arranging data in a systematic way (tables, lists, etc.).
- Presentation: Visualizing data using graphs (bar graphs, pie charts, line graphs, histograms) and pictographs.
- Analysis: Interpreting data to identify patterns, trends, and relationships.
- Measures of Central Tendency: Finding representative values like mean, median, and mode.
- Measures of Dispersion: Understanding data spread using range and other statistical measures.
By understanding these concepts, we can make sense of information, draw conclusions, and make informed decisions.
Exercise 4.1
1. A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey.
From this pie chart answer the following:
(i) If 20 people liked classical music, how many young people were surveyed?
(ii) Which type of music is liked by the maximum number of people?
(iii) If a cassette company were to make 1000 CDs. How many of each type would they make?
Ans :
The pie chart represents the preferences of a group of young people for different types of music:
- Classical: 10%
- Semi-classical: 20%
- Folk: 30%
- Light: 40%
Answering the Questions
(i)
- 10% of the total people surveyed liked classical music.
- If 20 people represent 10%, then the total number of people surveyed is:
- (20 people / 10%) * 100% = 200 people
(ii)
- Light music is liked by the maximum number of people, as it represents 40% of the total, which is the highest percentage among all music types.
(iii)
To find the number of CDs for each type, we need to calculate the corresponding percentage of 1000 CDs.
- Classical: 10% of 1000 = 100 CDs
- Semi-classical: 20% of 1000 = 200 CDs
- Folk: 30% of 1000 = 300 CDs
- Light: 40% of 1000 = 400 CDs
Therefore, the cassette company would make 100 Classical, 200 Semi-classical, 300 Folk, and 400 Light music CDs.
2. A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.
(i) Which season got the most votes?
(ii) Find the central angle of each sector.
(iii) Draw a pie chart to show this information.
Ans :
(i)
Winter got the most votes with 150 votes.
(ii)
To find the central angle for each sector, we need to calculate the percentage of votes for each season and then multiply it by 360 degrees (total angle of a circle).
- Total votes = 90 + 120 + 150 = 360
- Central angle for Summer: (90/360) * 360° = 90°
- Central angle for Rainy: (120/360) * 360° = 120°
- Central angle for Winter: (150/360) * 360° = 150°
(iii)
3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
Ans :
From the table, we have:
- Total number of people surveyed = 36
Calculating Central Angles To draw a pie chart, we need to find the central angle for each color.
- A total angle of circle is 360 degrees.
Formula: Central angle for a color = (Number of people who prefer that color / Total number of people) * 360
Calculations:
- Blue: (18/36) * 360 = 180 degrees
- Green: (9/36) * 360 = 90 degrees
- Red: (6/36) * 360 = 60 degrees
- Yellow: (3/36) * 360 = 30 degrees
4. The following pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.
(i) In which subject did the student score 105 marks?
(Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
(Hint: Just study the central angles).
Ans :
(i) Hindi.
(ii) Marks obtained by the student in Mathematics = (90/360)*540 = 135 Marks obtained by the student in Hindi = (70/360)*540 = 105 Difference = 135 – 105 = 30 So, the student obtained 30 more marks in Mathematics than in Hindi.
(iii) Marks obtained in Social Science and Mathematics
= (65/360)*540 + (90/360)*540
= 97.5 + 135 = 232.5
Marks obtained in Science and Hindi = (80/360)*540 + (70/360)*540
= 120 + 105 = 225 Yes, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
Ans :
- Hindi: (40/72) * 360 = 200 degrees
- English: (12/72) * 360 = 60 degrees
- Marathi: (9/72) * 360 = 45 degrees
- Tamil: (7/72) * 360 = 35 degrees
- Bengali: (4/72) * 360 = 20 degrees
Exercise 4.2
1. List the outcomes you can see in these experiments.
(i) Spinning a wheel
(ii) Tossing two coins together
Ans :
(i) Spinning a wheel:
The possible outcomes when spinning the wheel are the letters written on each section. Therefore, the outcomes are: A, B, C, D, and E.
(ii) Tossing two coins together:
When tossing two coins simultaneously, each coin can land on either heads (H) or tails (T). Thus, the possible outcomes are:
- HH (both heads)
- HT (first coin heads, second coin tails)
- TH (first coin tails, second coin heads)
- TT (both tails)
2. When a die is thrown, list the outcomes of an event of getting
(i) (a) a prime number
(b) not a prime number
(ii) (a) a number greater than 5
(b) a number not greater than 5
Ans :
(i) Outcomes of getting:
- (a) a prime number: 2, 3, 5
- (b) not a prime number: 1, 4, 6
(ii) Outcomes of getting:
- (a) a number greater than 5: 6
- (b) a number not greater than 5: 1, 2, 3, 4, 5
3. Find the
(i) Probability of the pointer stopping on D in (Question 1-(a))?
(ii) Probability of getting an ace from a well-shuffled deck of 52 playing cards?
(iii) Probability of getting a red apple, (see figure below)
Ans :
(i)
Probability of pointer stopping at D = 1/5
(ii)
4/52 = 1/13
A standard deck of 52 cards has 4 aces (one in each suit: spades, hearts, diamonds, and clubs). Therefore, the probability of drawing an ace is 4 out of 52 cards, which simplifies to 1/13.
(iii)
4/7
From the image, we can count a total of 7 apples, out of which 4 are red. Therefore, the probability of picking a red apple is 4 out of 7, or 4/7.
4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is choosen from the box without looking into it. What is the probability of:
(i) getting a number 6?
(ii) getting a number less than 6?
(iii) getting a number greater than 6?
(iv) getting a 1-digit number?
Ans :
(i)
- Favorable outcome: 1 (number 6)
- Probability = Number of favorable outcomes / Total number of outcomes
- = 1/10
(ii)
- Favorable outcomes: 1, 2, 3, 4, 5 (total 5 numbers)
- Probability = Number of favorable outcomes / Total number of outcomes
- = 5/10 = 1/2
(iii)
- Favorable outcomes: 7, 8, 9, 10 (total 4 numbers)
- Probability = Number of favorable outcomes / Total number of outcomes
- = 4/10 = 2/5
(iv)
- Favorable outcomes: 1, 2, 3, 4, 5, 6, 7, 8, 9 (total 9 numbers)
- Probability = Number of favorable outcomes / Total number of outcomes
- = 9/10
5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non-blue sector?
Ans :
Probability of getting a green sector
Total number of sectors: 3 (green) + 1 (blue) + 1 (red) = 5
Number of green sectors: 3
Probability:
Number of favorable outcomes / Total number of outcomes
= 3/5
Probability of getting a non-blue sector
Total number of sectors: 5
Number of non-blue sectors: 3 (green) + 1 (red) = 4
Probability:
Number of favorable outcomes / Total number of outcomes
= 4/5
Therefore, the probability of getting a green sector is 3/5, and the probability of getting a non-blue sector is 4/5.
6. Find the probabilities of the events given in Question 2.
Ans :
(i) (a) Probability of getting a prime number
(b) Probability of getting a non-prime number
(ii) (a) Probability of getting a number greater than 5 = ⅙
(b) Probability of a number not greater than 5 = ⅙ or, 1-⅙=⅚
