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**Maths Ace Class 8 Solutions Chapter 16 Data Handling**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Ace Prime Class 8 Math Book, Chapter 16, Data Handling. Here students can easily find step by step solutions of all the problems for Data Handling, Exercise 16.1, 16.2 and 16.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 16 solutions.

**Data Handling Exercise 16.1 Solution : **

**Question no – (1) **

**Solution : **

From the given data,

Observations : |
Tally marks : |
Frequency : |

1 | ||| | 3 |

2 | || | 2 |

3 | ||| | 3 |

4 | |||| | 4 |

5 | |||| | 5 |

6 | ||| | 3 |

**Question no – (2) **

**Solution : **

Now, from given data, frequency distribution table :

Observations : |
Tally marks : |
Frequency : |

15 – 20 | |||| || | 7 |

20 – 25 | |||| | 5 |

25 – 30 | |||| | 5 |

30 – 35 | |||| | 5 |

35 – 40 | |||| ||| | 8 |

Here, smallest observation = 15

largest observation = 39

Difference = (39 – 15) = 24

Divide in to 5 groups

**Question no – (3) **

**Solution : **

**(a)** What information does the graph represent?

= The graph represent the favourite subject of students in a class

**(b)** What does the y-axis represent?

= ‘Y’ axis represent the no of students

**(c)** How many students like Science?

= 75 students like science

**(d)** Which is the favourite subject of the students?

= Math’s is the favourite subject

**(e)** How many more students like English as compared to Social Studies?

= More students = (90 – 53)

= 35 students

**Question no – (4) **

**Solution : **

**(a)** What is the highest number of family members that are living in a house?

= Highest no of family members is 4

**(b)** How many people live alone?

= 8 people like alone

**(c)** How many houses have 6 family members?

= 4 houses have 6 family members

**(d)** What is the total number of houses in the society?

= Total no of houses 36

**(e)** What is the total number of people in the society?

= Total no of people 164.

**Question no – (5) **

**Solution : **

According to the question,

= (20 + 30 + 15 + 35)

= 70 units

There have no sale.

**Question no – (6) **

**Solution : **

**(a)** How many babies weigh 3 kg or above?

= 63

**(b)** How many babies are underweight if 3 kg is considered as the optimum value?

= 13

**(c)** Find the ratio of the number of babies weighing 5 kg or more but less than 6 kg to the number of babies weighing 3 kg or more but less than 4 kg.

= Ratio

= 5 : 25

= 1 : 5

**(d)** What percentage of babies weigh 3 kg or more but less than 4 kg?

= Percentage

= (25/75 × 100)

= 33.33%

**Question no – (7) **

**Solution : **

From given data,

Class Interval : |
Tally marks : |
Frequency : |

20 – 30 | |||| |||| |||| | 14 |

30 – 40 | |||| |||| | | 11 |

40 – 50 | |||| || | 7 |

50 – 60 | |||| || | 7 |

60 – 70 | | | 1 |

**(b)** 20 – 30 years of age group

**(c)** 14 teachers.

**Question no – (8) **

**Solution : **

**(a)** How many girls are less than 160 cm tall?

= 14 girls are less than 160 cm

**(b)** How many girls are 155 cm or taller?

= (15 + 5 + 7 + 7 + 3)

= 37

= 37 girls are 155 cm or taller

**Question no – (9) **

**Solution : **

Smallest observation = 0

Highest observation = 20

Frequency distribution table,

Class Interval : |
Tally marks : |
Frequency : |

0 – 5 | |||| | 5 |

5 – 10 | |||| |||| |||| | 15 |

10 – 15 | |||| |||| | 9 |

15 – 20 | |||| | 4 |

20 – 25 | |||| || | 7 |

**Question no – (10) **

**Solution : **

Lowest = 45

Highest = 99

(99 – 45) = 54

Now, 54/5 = 10.8 ≅ 11

Frequency distribution table,

Class Interval : |
Tally marks : |
Frequency : |

40 – 50 | | | 1 |

50 – 60 | ||| | 3 |

60 – 70 | ||| | 3 |

70 – 80 | |||| |||| | | 11 |

80 – 90 | |||| |||| | | 11 |

**Data Handling Exercise 16.2 Solution : **

**Question no – (1) **

**Solution : **

According to the question the given data are,

Subject : |
Marks : |

Hindi | 65 |

Science | 80 |

Social studies | 55 |

English | 70 |

Maths | 90 |

**Required pie chart is,**

**Question no – (2) **

**Solution : **

Bike = 110

Scooter = 130

Car = 100

Bus = 80

Bicycle = 180

—————————————-

Total = 600

**∴** Here 600 – 3600

= 1 – 3600/600

**Bike** = 110 – 360 × 110/600

= 660

**Scooter** = 130 – 360 × 130/600

= 780

**Car** = 100 = 360 × 100/600

= 600

**Bus **= 80 – 360 × 80/600

= 480

**Bicycle** = 180 – 360 × 180/600

= 108

**Question no – (3)**

**Solution : **

Blue = 400,

Red = 250,

Yellow = 350,

Green = 200

**∴** Total Color,

= (400 + 250 + 350 + 200)

= 1200

**Required pie chart :**

**Question no – (4) **

**Solution : **

Total people = 10000

**∴** Travel in Bus,

= 10000/360 × 450

= 1250 people

**∴** Travel in Train,

= 10000/360 × 72

= 2000 people

**∴ **Travel in Taxi

= 10000/360 × 72

= 2000 people

**∴ **Travel in Bicycle,

= 10000/360 × 171

= 4750 people

**Question no – (5) **

**Solution : **

According to the pie chart,

**(i)** Drink Banana shake,

= 1500/360 × 144

= 600

**(ii)** Drink Lemonade,

= 1500/360 × 72

= 300

**(iii)** Drink Iced tea,

= 1500/360 × 24

= 100

**(iv)** Drink Orange juice,

= 1500/360 × 96

= 400

**(v)** Drink Milk shake,

= 1500/3600 × 24

= 100

**(a)** Banana shake

**(b)** Iced tea and Milk shake

**(c)** 600 children

**(d)** (300 – 100) = 200 children.

**Question no – (6) **

**Solution : **

Total T-shirt sold = 10800

**(i)** T-shirt with size ‘XL’

= 10800/360 × 72

= 2160

**(ii)** T-shirt with size ‘M’

= 10800 /360 × 90

= 2700

**(iii)** T-shirt with size ‘L’

= 10800/360 × 108

= 3240

**(iv)** T-shirt with size ‘S’

= 10800/360 × 36

= 1080

**(v)** T-shirt with size ‘XXL’

= 10800/360 × 54

= 1620

**(b)** Difference,

= (2700 – 2160)

= 540

**(c)** ‘S’ size.

**Data Handling Exercise 16.3 Solution : **

**Question no – (1) **

**Solution : **

**(a)** Tossing two coins at once

= Sample space

= {HH, HT, TH, TT}

**(b)** Tossing a coin 4 times

= Sample space

= {HHHH, HHHT,HHTH, HTHH, THHH, HHTT, HTHT, THTH, TTHH, HTTH, HTTT, THHT, THTT, TTHT, TTTH, TTTT}

**(c)** Spinning a spinner on a wheel containing five colours-red, green, orange, yellow and blue

= Sample Space

= {Red, Orange, Green, Yellow, Blue}

**(d)** Rolling two dice simultaneously,

= Sample Space = { (1, 1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

**Question no – (2) **

**Solution : **

Probability,

= 4/52

= 1/13

Thus, the probability of drawing a king from a pack of playing cards is 1/13.

**Question no – (4) **

**Solution : **

As per the given question,

Obtaining a prime number from the numbers 1 to 50

**∴** Probability,

= 15/50

= 3/10

Therefore, the probability of obtaining a prime number will be 3/10.

**Question no – (5) **

**Solution :**

**∴** Probability of getting blue ball pen,

= 7/(7 + 5 + 12)

= 7/24

**∴** Probability of getting a red ball,

= 4/(7 + 4 + 12)

= 4/23

**∴ **Probability of not getting a red ball,

= (7 + 12)/23

= 19/23

**Question no – (6) **

**Solution : **

S = {HH, TT, HT, TH}

**∴** Probability of getting head both time,

= 1/4

**Question no – (7) **

**Solution : **

**∴** Total outcomes,

= (6 × 6)

= 36

**∴** Favorable outcomes,

= (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

= P(A) = 6/36

= 1/6

**Question no – (8) **

**Solution : **

Outcomes are,

= {(HHH), (HHT), (HTH), (THH), (TTT), (TTH), (THT), (HTT)}

Total = 8

**∴** Required probability of head to head,

= 4/8

= 1/2

Therefore, the probability of getting at least 2 heads will be 1/2.

**Question no – (9) **

**Solution : **

Here, n(s) = 36

Multiply of 3 = {(1, 2), (1,5), (2,1), (2,4), (3,3), (3,6), (4,2), (4,5), (5,1),(5,4), (6,3), (6,6)}

Total = 12

**∴** Probability,

= 12/36

= 1/3

Therefore, the probability of getting a sum as a multiple of 3 will be 1/3

**Previous Chapter Solution : **

👉 Chapter 1 👈