Class 7 Mathematics - Chapter 3: Data Handling (Exercise 3.1)
Welcome to Digital Pipal Academy! In this post, we will explore Exercise 3.1 from Class 7 General Mathematics - Chapter 3: Data Handling. This chapter focuses on understanding data, calculating averages, and determining ranges.
SCERT Assam Class 7 Maths Chapter 3 Solutions
| Exercise | Solution Link |
|---|---|
| Exercise 3.1 | Click Here |
| Exercise 3.2 | Click Here |
| Exercise 3.3 | Click Here |
| Exercise 3.4 | Click Here |
Exercise 3.1 Solutions
Question 1: Find the average and range of the first 10 natural numbers.
Solution:
We need to find the average (mean) and range of the first 10 natural numbers.
The first 10 natural numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Now,
Average`=\frac{\text{Sum of all numbers}}{\text{Total numbers}} `
`=\frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10}{10}`
`=\frac{55}{10}`
`=5.5`
Thus, the average of the first 10 natural numbers is 5.5.
Again,
The range is the difference between the largest and smallest number in
the given set.
Range`= \text{Largest number} - \text{Smallest number} `
`=10-1`
`=9`
Thus, the range of the first 10 natural numbers is 9.
Final Answer:
✅ Average
= 5.5
✅ Range = 9
Question 2. In a district level sports competition 12 schools participated. Prizes won by each school was as follows: 11, 8, 13, 6, 10, 15, 18, 9, 10, 9, 11, 12.
(i) What is the highest number of prizes won?
(ii) What is the lowest number of prizes won?
(iii) What is the range of data?
(iv) Find the arithmetic mean of the data?
Solution:
We are given the number of prizes won by 12 schools in a
district-level sports competition:
11, 8, 13, 6, 10, 15, 18, 9, 10, 9, 11, 12
Now, we will find the required values step by step.
(i) Highest number of prizes won
The highest number in the given data is 18.
✅ Highest number of prizes = 18
(ii) Lowest number of prizes won
The lowest number in the given data is 6.
✅ Lowest number of prizes = 6
(iii) Range of the data
The range is calculated as:
Range`= \text{Largest number} - \text{Smallest number} `
`=18-6`
`=12`
✅ Range = 12
(iv) Arithmetic Mean (Average)
The formula for the arithmetic mean is:
Mean`= \frac{\text{Sum of all values}}{\text{Total number of values}} `
Mean`= \frac{11+8+13+6+10+15+18+9+10+9+11+12}{12} `
Mean`= \frac{132}{12} `
Mean`=11`
✅ Arithmetic Mean = 11
Question 3: In an Evaluation a student obtained following marks (out of 100)
A student scored the following marks out of 100:
- Mathematics: 75
- Assamese: 73
- Science: 82
- Social Science: 69
- English: 67
- Hindi: 78
Find the average of the marks obtained?
Solution:
Average Marks`= \frac{75+73+82+69+67+78}{6} `
Average Marks`= \frac{444}{6}`
Average Marks`=74`
Question 4. The number of HSLC examination passed out student of a school in last five years are 40, 62, 68, 48, 52 respectively. Find the average of the successful students.
Solution:
We are given the number of HSLC examination passed students in the last five years:
40, 62, 68, 48, 52
Now, we need to find the average (mean) number of successful students.
The formula for the average is:
Average`=\frac{\text{Sum of all numbers}}{\text{Total numbers}} `
`=\frac{\text{40+62+68+48+52}}{\text{5}} `
`=\frac{\text{270}}{\text{5}} `
`=54`
Final Answer:
✅ Average number of successful students = 54
Question 5: A cricket player scored runs in 8 innings as follows: 77, 41, 101, 46, 59, 1, 36, 47. What is the average score of the player?
Solution:
We are given the runs scored by a cricket player in 8 innings:
77, 41, 101, 46, 59, 1, 36, 47
Now, we need to find the average (mean) score of the player.
The formula for the average is:
Average`=\frac{\text{Sum of all numbers}}{\text{Total numbers}} `
`=\frac{\text{77+41+101+46+59+1+36+47}}{\text{8}} `
`=\frac{\text{408}}{\text{8}} `
`=51`
Final Answer:
✅ Average score of the player = 51
Question 6: Weight of 7 boys are as follows 36 kg, 32 kg, 30 kg, 28 kg, 32 kg, 33 kg, 26 kg.
(i) Find the average weight of the boys?
(ii) How many boys are there having weights more than 30 kg?
(iii) Is there any boy in the table whose weight is less than 25 kg? If yes what is the number of them?
Solution:
We are given the weights of 7 boys:
36 kg, 32 kg, 30 kg, 28 kg, 32 kg, 33 kg, 26 kg
Now, we will find the required values step by step.
(i) Find the Average Weight
The formula for average (mean) weight is:
Average`=\frac{\text{Sum of all numbers}}{\text{Total numbers}} `
`=\frac{\text{36+32+30+28+32+33+26}}{\text{7}} `
`=\frac{\text{217}}{\text{7}} `
`=31`
✅ Average weight of the boys = 31 kg
(ii) Number of Boys Having Weight More Than 30 kg
From the given weights, the boys having weights more than 30 kg are:
36 kg, 32 kg, 32 kg, 33 kg
Total = 4 boys
✅ Number of boys with weight more than 30 kg = 4
(iii) Is There Any Boy with Weight Less Than 25 kg?
Looking at the given weights: 36, 32, 30, 28, 32, 33, 26, we see that all weights are 26 kg or more.
So, there is no boy with weight less than 25 kg.
✅ No boy has a weight less than 25 kg
Solution:
We are given Mira's deposits in the last 5 months:
Rs. 500, Rs. 600, Rs. 600, Rs. 700, Rs. 500
Now, we need to find her average deposit per month.
`= \frac{\text{Sum of all deposits}}{\text{Total number of months}}`
`= \frac{\text{500+600+600+700+500}}{\text{5}}`
`=580`
Final Answer:
✅ Mira’s average deposit per month = Rs. 580
Question 8: Students of a Primary School of different classes are as follow:
| Class I | Class II | Class III | Class VI | Class V |
|---|---|---|---|---|
| 26 | 32 | 34 | 28 | 30 |
(i) What is the average number of student in the classes of the school?
(ii) After first Periodical Evaluation 3 and 2 students were admitted to class II and V respectively. Find the new average number of student of classes of the school?
Solution:
(i) Find the Average Number of Students in the Classes
The formula for average (mean) is:
`=\frac{\text{Sum of all students}}{\text{Total number of classes}}`
`=\frac{\text{26+32+34+28+30}}{\text{5}} `
`=\frac{\text{150}}{\text{5}} `
`=30`
✅ Average number of students in the classes = 30
(ii) Find the New Average After Admissions
After first Periodical Evaluation,
- 3 students were admitted to Class II
- 2 students were admitted to Class V
Thus, the new student count becomes:
| Class | Class I | Class II | Class III | Class VI | Class V |
|---|---|---|---|---|---|
| Students | 26 | (32 + 3) = 35 | 34 | 28 | (30 + 2) = 32 |
New Average`=\frac{\text{155}}{\text{5}} `
`=31`
✅ New average number of students in the classes = 31
Final Answer:
✅ Initial average number of
students = 30
✅ New average number of students after admission = 31
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