1(i)
Arrange the following data in ascending order:
8, 3, 11, 15, 1, 7, 16, 25, 9, 4.
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Arranging the given data in ascending order, we get:
1, 3, 4, 7, 8, 9, 11, 15, 16, 25.
Data Handling
ICSE Class 6 Mathematics · Solutions for Class 6 RS Aggarwal ICSE Foundation Mathematics · 16 solved questions
1(ii)
Arrange the following data in ascending order:
5.7, 9.2, 3.1, 4.6, 1.8, 10.4, 2.5, 0.9, 1.2.
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Arranging the given data in ascending order, we get:
0.9, 1.2, 1.8, 2.5, 3.1, 4.6, 5.7, 9.2, 10.4.
2(i)
Arrange the following data in descending order:
15, 3, 0, 11, 7, 2, 23, 14, 29, 5, 1, 17.
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Arranging the given data in descending order, we get:
29, 23, 17, 15, 14, 11, 7, 5, 3, 2, 1, 0.
2(ii)
Arrange the following data in descending order:
2.3, 4.6, 1.2, 0.4, 3.5, 9.7, 6.1, 4.8, 0.8, 1.0.
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Arranging the given data in descending order, we get:
9.7, 6.1, 4.8, 4.6, 3.5, 2.3, 1.2, 1.0, 0.8, 0.4.
3
The number of children in 30 families of a colony are given below:
1, 2, 0, 3, 3, 2, 2, 1, 1, 1, 0, 0, 2, 3, 4, 1, 2, 3, 3, 0, 4, 2, 2, 3, 3, 1, 1, 2, 2, 3
Represent the above data in the form of a frequency table.
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Arranging the given data in ascending order, we get:
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4
The frequency distribution table for the given data is:
| Number of children | Tally marks | Number of families (Frequency) |
|---|---|---|
| 0 | IIII | 4 |
| 1 | IIII II | 7 |
| 2 | IIII IIII | 9 |
| 3 | IIII III | 8 |
| 4 | II | 2 |
4
The sale of shoes of various sizes at a shop on a particular day is given below:
6, 9, 8, 5, 5, 4, 9, 8, 5, 6, 9, 9, 7, 8, 9, 7, 6, 9, 8, 6, 7, 5, 8, 9, 4, 5, 8, 7
Represent the above data in the form of a frequency table.
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Arranging the given data in ascending order, we get:
4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9
The frequency distribution table for the given data is:
| Shoe-size | Tally marks | Number of shoes sold (Frequency) |
|---|---|---|
| 4 | II | 2 |
| 5 | IIII | 5 |
| 6 | IIII | 4 |
| 7 | IIII | 4 |
| 8 | IIII I | 6 |
| 9 | IIII II | 7 |
5
Construct a frequency table for the following:
3, 2, 1, 3, 5, 4, 3, 2, 2, 1, 1, 2, 1, 3, 5, 2, 2, 3, 1, 4, 5, 2, 3
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Arranging the given data in ascending order, we get:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5
The frequency distribution table for the given data is:
| Observation | Tally marks | Frequency |
|---|---|---|
| 1 | IIII | 5 |
| 2 | IIII II | 7 |
| 3 | IIII I | 6 |
| 4 | II | 2 |
| 5 | III | 3 |
6
Construct a frequency table for the following:
6, 7, 8, 7, 5, 10, 9, 8, 8, 7, 6, 7, 10, 8, 9, 7, 7, 6, 5, 6, 8, 7
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Arranging the given data in ascending order, we get:
5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10
The frequency distribution table for the given data is:
| Observation | Tally marks | Frequency |
|---|---|---|
| 5 | II | 2 |
| 6 | IIII | 4 |
| 7 | IIII II | 7 |
| 8 | IIII | 5 |
| 9 | II | 2 |
| 10 | II | 2 |
1
Assertion (A): An observation occurring six times in a data is represented as IIII I.
Reason (R): To make counting convenient, we write tally marks in bunches of five, the 5th one crossing diagonally.
- (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- (c)Assertion (A) is true but Reason (R) is false.
- (d)Assertion (A) is false but Reason (R) is true.
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To make counting convenient, tally marks are written in bunches of five, the 5th one crossing the four diagonally. So, an observation occurring six times is represented by one bunch of five tally marks and one more tally mark, i.e., IIII I.
So, Assertion (A) is true.
To make counting convenient, we write tally marks in bunches of five, the 5th one crossing diagonally.
So, Reason (R) is true.
Since the representation in Assertion (A) follows the rule of writing tally marks in bunches of five given in Reason (R), Reason (R) correctly explains Assertion (A).
∴ Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Hence, option 1 is the correct option.
2
Assertion (A): The number of times a particular observation occurs in a given data is called its frequency.
Reason (R): A data is a collection of numbers gathered to give some meaningful information.
- (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- (c)Assertion (A) is true but Reason (R) is false.
- (d)Assertion (A) is false but Reason (R) is true.
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The number of times a particular observation occurs in a given data is called its frequency.
So, Assertion (A) is true.
A data is a collection of numbers gathered to give some meaningful information.
So, Reason (R) is true.
Reason (R) only tells what a data is. It does not explain what frequency of an observation is. So, Reason (R) does not explain Assertion (A).
∴ Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Hence, option 2 is the correct option.
1
Given below are the marks scored (out of 40) by 30 students of class 6 in a Science test.
18, 21, 26, 39, 27, 30, 25, 20, 12, 15, 19, 36, 32, 37, 11, 31, 27, 23, 20, 24, 29, 30, 26, 37, 14, 15, 26, 30, 18, 33
How many students scored more than 25 but less than 30 marks?
- (a)6
- (b)7
- (c)8
- (d)9
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Arranging the given marks in ascending order, we get:
11, 12, 14, 15, 15, 18, 18, 19, 20, 20, 21, 23, 24, 25, 26, 26, 26, 27, 27, 29, 30, 30, 30, 31, 32, 33, 36, 37, 37, 39
The marks more than 25 but less than 30 are 26, 26, 26, 27, 27 and 29.
∴ Number of students who scored more than 25 but less than 30 marks = 6
Hence, option 1 is the correct option.
2
Given below are the marks scored (out of 40) by 30 students of class 6 in a Science test.
18, 21, 26, 39, 27, 30, 25, 20, 12, 15, 19, 36, 32, 37, 11, 31, 27, 23, 20, 24, 29, 30, 26, 37, 14, 15, 26, 30, 18, 33
What is the difference between the highest and the lowest marks scored?
- (a)25
- (b)27
- (c)28
- (d)29
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From the given data,
Highest marks scored = 39
Lowest marks scored = 11
∴ Difference between the highest and the lowest marks = 39 − 11 = 28
Hence, option 3 is the correct option.
3
The given table shows the number of books read by Ashima in six months.
| Months | Tally marks |
|---|---|
| 1 | IIII IIII IIII |
| 2 | IIII IIII |
| 3 | IIII II |
| 4 | IIII I |
| 5 | IIII |
| 6 | IIII III |
I. How many total books did she read in these six months?
II. Find the fraction of number of books read in the month 2 to the number of books read in the months 4 and 6 together.
- (a)I: 49, II: $\frac{11}{14}$
- (b)I: 49, II: $\frac{9}{14}$
- (c)I: 54, II: $\frac{7}{11}$
- (d)I: 54, II: $\frac{11}{15}$
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Counting the tally marks, the number of books read by Ashima in each month is:
| Months | Tally marks | Number of books read |
|---|---|---|
| 1 | IIII IIII IIII | 14 |
| 2 | IIII IIII | 9 |
| 3 | IIII II | 7 |
| 4 | IIII I | 6 |
| 5 | IIII | 5 |
| 6 | IIII III | 8 |
I. Total number of books read in six months = 14 + 9 + 7 + 6 + 5 + 8 = 49
II. Number of books read in month 2 = 9
Number of books read in months 4 and 6 together = 6 + 8 = 14
∴ Required fraction = $\frac{9}{14}$
Hence, option 2 is the correct option.
4
Sarita made the frequency table to show the number of times each vowel was used in the first sentence of several books she had read. Which of the following lists shows the vowels in order of the most used to the least used?
| Vowels | Tally marks |
|---|---|
| A | IIII IIII |
| E | IIII III |
| I | IIII |
| O | IIII II |
| U | II |
- (a)U, I, E, O, A
- (b)E, I, A, O, U
- (c)A, E, O, I, U
- (d)A, E, I, O, U
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Counting the tally marks, the number of times each vowel was used is:
| Vowels | Tally marks | Frequency |
|---|---|---|
| A | IIII IIII | 9 |
| E | IIII III | 8 |
| I | IIII | 5 |
| O | IIII II | 7 |
| U | II | 2 |
Arranging the frequencies from the most used to the least used, we get:
9 (A), 8 (E), 7 (O), 5 (I), 2 (U)
∴ The vowels in order of the most used to the least used are A, E, O, I, U.
Hence, option 3 is the correct option.
5
The given table shows the number of T-shirts sold by a shopkeeper on 5 days of a week.
| Days | Tally marks |
|---|---|
| Monday | IIII IIII IIII II |
| Tuesday | IIII IIII I |
| Wednesday | IIII II |
| Thursday | IIII |
| Friday | IIII II |
The number of T-shirts sold on Monday is more than the number of T-shirts sold on Friday by:
- (a)5
- (b)10
- (c)17
- (d)8
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Counting the tally marks, we get:
Number of T-shirts sold on Monday (IIII IIII IIII II) = 5 + 5 + 5 + 2 = 17
Number of T-shirts sold on Friday (IIII II) = 5 + 2 = 7
∴ Number of T-shirts sold on Monday more than on Friday = 17 − 7 = 10
Hence, option 2 is the correct option.
6
The marks (out of 100) obtained by 28 students in a test are listed as below:
80, 10, 20, 60, 50, 50, 50, 10, 10, 90, 70, 80, 10, 50, 80, 30, 10, 80, 100, 100, 30, 40, 80, 70, 80, 90, 20, 100.
The number of students who obtained more than or equal to 50 marks is:
- (a)13
- (b)18
- (c)16
- (d)17
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Arranging the given marks in ascending order, we get:
10, 10, 10, 10, 10, 20, 20, 30, 30, 40, 50, 50, 50, 50, 60, 70, 70, 80, 80, 80, 80, 80, 80, 90, 90, 100, 100, 100
The frequency of each mark of 50 or more is:
| Marks | Tally marks | Number of students (Frequency) |
|---|---|---|
| 50 | IIII | 4 |
| 60 | I | 1 |
| 70 | II | 2 |
| 80 | IIII I | 6 |
| 90 | II | 2 |
| 100 | III | 3 |
∴ Number of students who obtained more than or equal to 50 marks = 4 + 1 + 2 + 6 + 2 + 3 = 18
Hence, option 2 is the correct option.
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