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**OP Malhotra Class 9 ICSE Maths Solutions Chapter 15 Mean Median and Frequency Polygon**

Welcome to NCTB Solutions. Here with this post we are going to help 9th class students for the Solutions of OP Malhotra Class 9 ICSE Math Book, Chapter 15, Mean, Median and Frequency Polygon. Here students can easily find step by step solutions of all the problems for Mean, Median and Frequency Polygon, Exercise 15a, 15b and 15c 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 15 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

**Mean, Median and Frequency Polygon Exercise 15(a) Solution :**

**Question no – (1) **

**Solution : **

**(i) Frist 5 natural numbers**

**∴** Mean of 1^{st} 5 natural numbers

= 1 + 2 +3 + 4 + 5/5

= 15/5

= 3

**(ii) Frist 7 whole numbers**

**∴** Mean of 1^{st} 7 whole numbers are

= 0 + 1 + 2 + 3 + 4 + 5 + 6/7

= 21/7

= 3

**(iv) Frist 4 prime numbers**

**∴** Mean of 1^{st} 4 prime No is

= 2 + 3 + 5 + 7/4

= 17/4

= 4.24

**(iv) 1.3 cm, 5.7 cm, 89,8 cm, 6.4 cm, 6.9 cm**

**∴** Mean = 1.3 + 5.7 + 9.8 + 6.4 + 6.9/5

= 30.1/5

= 6.02 cm

**(v) Rs 7, Rs 19, Rs 31, Rs 43, Rs 70**

**∴** Mean = (7 + 19 + 31 + 43 + 70/5) Rs

= 170/5

= 70

**Question no – (2) **

**Solution : **

As per the question, Seema’s scores are, 80, 85, 90, 71, 60, 100.

**∴**** Seema Mean Score, **

= 80 + 85 + 90 + 71 + 60 + 100/6

= 486/6

= 81

Therefore, her mean score will be 81.

**Question no – (3) **

**Solution : **

According to the question,

Shaleen’s last six batting scores were 138, 144, 155, 142, 167, 172

**∴**** Mean of batting score,**

= 13.8 + 144 + 155 + 142 + 167 + 172/6

= 918/6

= 153

Therefore, his mean score will be 153.

**Question no – (4) **

**Solution : **

As per the question we know,

Madhu worked 2 hours on Monday,

2 1/2 hours on Monday,

3 1/4 hrs on Tuesday,

2 3/4 hrs on Wednesday

**∴**** Mean of working hour, **

= 2 1/2 + 3 1/4 + 2 3/4/3

= 7 + (1/23 + 1/4 + 3/4)/3

= 7 + (2 + 1 + 3/4)/3

= 7 + 6/4

= 7 6/4/3

= 7 2/3/3

= 17/2 / 3

= 17/6

= 2 5/6

Therefore, she worked 2 5/6 mean number of hours.

**Question no – (5) **

**Solution : **

**Mean of Ayushree score,**

= 68 + 75 + 70 + 45 + 57 + 77/6

= 392/6

= 65.33%

**Mean of Aanaya score,**

= 52 + 87 + 64 + 53 + 74 + 81 + 86/7

= 497/7

= 71%

Therefore, Ananya has highest mean score.

**Question no – (6) **

**Solution : **

As we know that,

First 10 odd natural numbers are **1, 3, 5, 7, 9, 11, 13, 15, 17, 19**

Mean of 1^{st} 10 odd natural numbers,

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19/10

= 100/10

= 10

Thus, the Mean of 1^{st} 10 odd natural numbers is 10

**Question no – (7) **

**Solution : **

**Sum of 5 marks given, **

= 16 + 14 + x + 23 + 20

= 73 + x

**Total of 5 no is** = 5 × 18 = 90

**∴** 73 + x = 90

= x = 90 – 73

= 17

Therefore, the value will be 17

**Question no – (8) **

**Solution : **

Here, total t terms,

= 24 × 5

= 120

**Sum of Mean, **

= x + x + 2 + x + 4 + x + 6 + x + 8

= 5x + 20

**∴** 5x + 20 = 120

= 5x = 120 – 20

= 100

= x = 100/5

= 20

Therefore, x will be 20

**Question no – (9)**

**Solution : **

**From the given question we know, **

Madhu practiced on her sitar

45 minutes,

30 minutes,

60 minutes,

50 minutes

20 minutes

**∴**** Mean practice time, **

= 45 + 30 + 60 + 50 + 20/5

= 205/5

= 41 min

Hence, her mean practice time will be 41 min.

**Question no – (10) **

**Solution : **

Let, marks = x

= 73 + 86 + 78 + 75 + x/5

= 312 + x/5

**∴** Here Mean score is 80

Now, 312 + x/5 = 80

= 31 + x = 400

= x = 400 – 312

= 88 marks

Therefore, the least number of marks Nisha can secure will be 88 marks.

**Question no – (11) **

**Solution : **

Here, Total runs,

= (60 × 10) = 600 runs of runs of 11 innings

= 11 × 62

= 682 runs

**∴**** Number of runs scored in 11**^{th}** innings,**

= 682 – 600

= 82 runs

Therefore, 88 runs are to be scored in the eleventh innings.

**Question no – (12) **

**Solution : **

Weight (x) |
Number of students (f) |
(f x_{0}) |

30 | 8 | 240 |

31 | 10 | 310 |

32 | 15 | 480 |

33 | 8 | 264 |

34 | 9 | 306 |

Total |
50 | 1600 |

**∴ Mean,**

= 1600/50

= 32 kg

Therefore, the mean of the given frequency distributions will be 32 kg.

**Question no – (13) **

**Solution : **

X |
F |
F×^{x} |

2 | ||

5 | ||

7 | ||

8 | ||

Total |
15 | 90 |

**∴ Mean,**

= 90/15

= 6

Therefore, the mean of the given frequency distribution will be 6.

**Question no – (14) **

**Solution : **

According to the question,

X |
F |
Fx |

0.1 | 20 | 2 |

0.2 | 60 | 12 |

0.3 | 20 | 6 |

0.4 | 40 | 16 |

0.5 | 10 | 5 |

0.6 | 50 | 30 |

Total | 200 | 71 |

**∴ Mean,**

= 200/71

= 0.355

Therefore, the mean of the given frequency distribution will be 0.355.

**Next Chapter Solution : **

👉 Chapter 16 👈