## NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Topics and Sub Topics in Class 11 Maths Chapter 15 Statistics:

Section Name | Topic Name |

15 | Statistics |

15.1 | Introduction |

15.2 | Measures of Dispersion |

15.3 | Range |

15.4 | Mean Deviation |

15.5 | Variance and Standard Deviation |

15 .6 | Analysis of Frequency Distributions |

### NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1

**Question 1:**

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**Question 2:**

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**More Resources for CBSE Class 11**

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### Class 11 Maths NCERT Solutions – Miscellaneous Questions

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**Exercise 15.1**

**Q1. Calculate the mean deviation about the mean for the given data**

**5, 8, 9, 10, 11, 13, 14, 18**

**Q2**. **Calculate the mean deviation about the mean for the given data**

**39, 71, 49, 41, 43, 56, 64, 47, 55, 45**

**Q3.** **Calculate the mean deviation about the median for the given data:**

**13, 16, 11, 10, 11, 12, 17, 14, 13, 16, 18, 17**

**Q4. Calculate the mean deviation about the median for the given data:**

**36, 46, 60, 53, 51, 72, 42, 45, 46, 49**

**Q5. Calculate the mean deviation about the mean for the given data**

** **

xi | 5 | 10 | 15 | 20 | 25 |

fi | 7 | 4 | 6 | 3 | 5 |

**Q6. Calculate the mean deviation about the mean for the given data**

xi | 10 | 10 | 15 | 20 | 25 |

fi | 7 | 4 | 6 | 3 | 5 |

**Q7. Calculate the mean deviation about the median for the given data**

xi | 10 | 10 | 15 | 20 | 25 |

fi | 7 | 4 | 6 | 3 | 5 |

xi | 5 | 7 | 9 | 10 | 12 | 15 |

fi | 8 | 6 | 2 | 2 | 2 | 6 |

**Q8. Calculate the mean deviation about the median for the given data**

xi | 15 | 21 | 27 | 30 | 35 |

fi | 3 | 5 | 6 | 7 | 8 |

**Q9. Calculate the mean deviation about the mean for the given data:**

Income per day | Number of persons |

0 – 100 | 4 |

100 – 200 | 8 |

200 – 300 | 9 |

300 – 400 | 10 |

400 – 500 | 7 |

500 – 600 | 5 |

600 – 700 | 4 |

700 – 800 | 3 |

**Q10. Calculate the mean deviation about the mean for the given data:**

Height in cm | Number of boys |

95 – 105 | 9 |

105 – 115 | 13 |

115 – 125 | 26 |

125 – 135 | 30 |

135 – 145 | 12 |

145 – 155 | 10 |

**Q11. Calculate the mean deviation about the median for the given data:**

Marks | Number of girls |

0 – 10 | 6 |

10 – 20 | 8 |

20 – 30 | 14 |

30 – 40 | 16 |

40 – 50 | 4 |

50 – 60 | 2 |

**Q12. Calculate the mean deviation about the median for the given data:**

** **** **

Age | Number |

16 – 20 | 5 |

21 – 25 | 6 |

26 – 30 | 12 |

31 – 35 | 14 |

36 – 40 | 26 |

41 – 45 | 12 |

46 – 50 | 16 |

51 – 55 | 9 |

**Exercise 15.2**

**Q1. Calculate mean and variance for the given data 6, 7, 10, 12, 13, 4, 8, 12**

**Q2. Calculate the mean and variance for the first n natural numbers.**

**Q3. Calculate the mean and variance for the first 10 multiples of 3.**

**Q4. Calculate the mean and variance for the data**

xi | 6 | 10 | 14 | 18 | 24 | 28 | 30 |

fi | 2 | 4 | 7 | 12 | 8 | 4 | 3 |

**Q5. Calculate the mean and variance for the data**

xi | 92 | 93 | 97 | 98 | 102 | 104 | 109 |

fi | 3 | 2 | 3 | 2 | 6 | 3 | 3 |

**Q6. Calculate the mean and standard deviation using short-cut method.**

** **

xi | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 |

fi | 2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |

**Q7. Calculate the mean and variance for the given frequency distribution.**

** **

Classes | 0 – 30 | 30 – 60 | 60 – 90 | 90 – 120 | 120 – 150 | 150 – 180 | 180 – 210 |

Frequencies | 2 | 3 | 5 | 10 | 3 | 5 | 2 |

**Q8. Calculate the mean and variance for the following frequency distribution.**

Classes | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |

Frequencies | 5 | 8 | 15 | 16 | 6 |

**Q9. Calculate the mean, variance and standard deviation using short – cut method:**

** **

Height in cm | Number of children |

70 – 75 | 3 |

75 – 80 | 4 |

80 – 85 | 7 |

85 – 90 | 7 |

90 – 95 | 15 |

95 – 100 | 9 |

100 – 105 | 6 |

105 – 110 | 6 |

110 – 115 | 3 |

**Q10. The diameters of circles (in mm) drawn in a design are given below:**

Diameters | Number of Children |

33 – 36 | 15 |

37 – 40 | 17 |

41 – 44 | 21 |

45 – 48 | 22 |

49 – 52 | 25 |

**Exercise 15.3**

**Q1. From the data given below state which group is more variable, A or B**** **

Marks | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 |

Group A | 9 | 17 | 32 | 33 | 40 | 10 | 9 |

Group B | 10 | 20 | 30 | 25 | 43 | 15 | 7 |

**Q2. From the prices of shares X and Y below, find out which is more stable in value.**

X | 35 | 54 | 52 | 53 | 56 | 58 | 52 | 50 | 51 | 49 |

Y | 108 | 107 | 105 | 105 | 106 | 107 | 104 | 103 | 104 | 101 |

**Q3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:**

| Firm A | Firm B |

No. of wage earners | 586 | 648 |

Mean of monthly wages | Rs. 5253 | Rs. 5253 |

Variance of the distribution of wages | 100 | 121 |

**(i) Which firm A or B pays larger amount as monthly wages?**

**(ii) Which firm, A or B, shows greater variability in individual wages?**

**Q4. The following is the record of goals scored by team A in a football session:**

** **

Number of goals scored | 0 | 1 | 2 | 3 | 4 |

Number of matches | 1 | 9 | 7 | 5 | 3 |

**For the team B, mean number of goals scored per match was 2 with standard deviation 1.25 goals. Find which team may be considered more consistent?**

### NCERT Solutions for Class 11 Maths All Chapters

- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutation and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability