### NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.1

**Ex 3.1 Class 7 Maths Question 1.**

**Find the range of heights of any ten students of your class.**

**Solution:**

Let us have the heights of 10 students are as follows:

140 cm, 141.5 cm, 138 cm, 150 cm, 161 cm,

138 cm, 140.5 cm, 135.5 cm, 160 cm, 158 cm

Here, minimum height = 135.5 cm

Maximum height =161 cm

∴ Range = Maximum height – Minimum height

= 161 cm — 135.5 cm = 25.5 cm

Hence, the required range = 25.5 cm.

**Ex 3.1 Class 7 Maths Question 2.**

**Organise the following marks in a class assessment in a tabular form.**

**4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7**

**(i) Which number is the highest?**

**(ii) Which number is the lowest?**

**(iii) What is the range of the data?**

**(iv) Find the arithmetic mean.**

**Solution:**

Let us form a frequency distribution table:

**Ex 3.1 Class 7 Maths Question 4.**

**A cricketer scores the following runs in eight innings:**

**58, 76, 40, 35, 46, 45, 0, 100**

**Find the mean score.**

**Solution:**

Following are the scores of the runs in eight innings:

58, 76, 40, 35, 46, 45, 0, 100

∴ Mean

Hence, the required mean = 50.

**Ex 3.1 Class 7 Maths Question 5.**

**Following table shows the points of each player scored in four games:**

Player | Game 1 | Game 2 | Game 3 | Game 4 |

A | 14 | 16 | 10 | 10 |

B | 0 | 8 | 6 | 4 |

C | 8 | 11 | Did not play | 13 |

**Now answer the following questions:**

**(i) Find the mean to determine A’s average number of points scored per game.**

**(ii) To find the mean number of points per game for C, would you divide the total points by 3 or by 4? Why?**

**(iii) B played in all the four games. How would you find the mean?**

**(iv) Who is the best performer?**

**Solution:**

(i) Number of points scored by A in all games are

Game 1 – 14, Game 2 = 16, Game 3 = 10, Game 4 = 10

∴ Average score

(ii) Since, C did not play Game 3, he played only 3 games. So, the total will be divided by 3.

(iii) Number of points scored by B in all the games are Game 1 = 0, Game 2 = 8, Game 3 = 6, Game 4 = 4

∴ Average score =

(iv) Mean score of C

Mean score of C = 10.67

While mean score of A = 12.5

Clearly, A is the best performer.

**Ex 3.1 Class 7 Maths Question 6.**

**The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the**

**(i) highest and the lowest marks obtained by the students.**

**(ii) range of the marks obtained.**

**(iii) mean marks obtained by the group.**

**Solution:**

Marks obtained are:

85, 76, 90, 85, 39, 48, 56, 95, 81 and 75

(i) Highest marks = 95

Lowest marks = 39

(ii) Range of the marks

= Highest marks – Lowest marks

= 95 – 39 = 56

(iii) Mean marks

**Ex 3.1 Class 7 Maths Question 7.**

**The enrolment in a school during six consecutive years was as follows:**

**1555, 1670, 1750, 2013, 2540, 2820**

**Find the mean enrolment of the school for this period.**

**Solution:**

Mean enrolment

Thus, the required mean = 2058.

**Ex 3.1 Class 7 Maths Question 8.**

**The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows**

Day | Rainfall (in mm) |

Monday | 0.0 |

Tuesday | 12.2 |

Wednesday | 2.1 |

Thursday | 0.0 |

Friday | 20.5 |

Saturday | 5.5 |

Sunday | 1.0 |

**(i) Find the range of the rainfall in the above data.**

**(ii) Find the mean rainfall for the week.**

**(iii) On how many days was the rainfall less than the mean rainfall?**

**Solution:**

(i) Maximum rainfall = 20.5 mm

Minimum rainfall = 0.0 mm

∴ Range = Maximum rainfall – Minimum rainfall

= 20.5 mm – 0.0 mm = 20.5 mm

(ii) Mean rainfall

(iii) Number of days on which the rainfall was less than the mean rainfall = Monday, Wednesday, Thursday, Saturday, Sunday = 5 days.

**Ex 3.1 Class 7 Maths Question 9.**

**The heights of 10 girls were measured in cm and the results are as follows:**

**135, 150, 139, 128, 151, 132, 146, 149, 143, 141**

**(i) What is the height of the tallest girl?**

**(ii) What is the height of the shortest girl?**

**(Hi) What is the range of the data?**

**(iv) What is the mean height of the girls?**

**(v) How many girls have heights more than the mean height?**

**Solution:**

(i) Height of the tallest girl = 151 cm.

(ii) Height of the shortest girl = 128 cm.

(iii) Range = Height of tallest girl – Height of the shortest girl

= 151 cm – 128 cm = 23 cm.

(v) Number of girls having more height than the mean height

= 150, 151, 146, 149 and 143 = 5 girls