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NCERT Exemplar Class 11 Maths Chapter 15 Statistics

June 20, 2022 by Sastry CBSE

NCERT Exemplar Class 11 Maths Chapter 15 Statistics are part of NCERT Exemplar Class 11 Maths. Here we have given NCERT Exemplar Class 11 Maths Chapter 15 Statistics.

NCERT Exemplar Class 11 Maths Chapter 15 Statistics

Short Answer Type Questions

Q1. Find the mean deviation about the mean of the distribution:

Size 20 21 22 23 24
Frequency 6 4 5 1 4

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 1

Q2. Find the mean deviation about the median of the following distribution:

Marks obtained 10 11 12 14 15
Number of students 2 3 8 3 4

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 2

Q3. Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number.
Sol: Consider first natural number when n is an odd i.e., 1, 2, 3,4,… , n [odd].
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 3
Q4. Calculate the mean deviation about the mean of the set of first n natural numbers when n is an even number.
Sol: Consider first n natural number, when n is even i.e., 1, 2, 3,4..n.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 4

Q5. Find the standard deviation of the first n natural numbers.

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 5
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 6

Q6. The mean and standard deviation of some data for the time taken to complete . a test are calculated with the following results:
Number of observations = 25, mean = 18.2 seconds, standard deviation = 3.25 s.

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 7
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 8
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 9
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 10
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 11

Q8. Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 12

Q9. The frequency distribution:

X A 2A 3 A 4A 5 A 6A
f 2 1 1 1 1 1

where A is a positive integer, has a variance of 160. Determine the value of A.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 13

Q10. For the frequency distribution:

X 2 3 4 5 6 7
f 4 9 16 14 11 6

Find the standard deviation.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 14
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 15

Q11. There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test:

Marks 0 i 2 3 4 5
Frequency x – 2 X x2 (x+1)2 2x x + 1

where x is a positive integer. Determine the mean and standard deviation of the marks.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 16

Q12. The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 17

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 18

Q13. Mean and standard deviation of 100 items are 50 and 4, respectively. Then find the sum of all the item and the sum of the squares of the items.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 19

Q14. If for a distribution Σ (x -5)= 3,Σ (x -5)2= 43 and the total number of item is 18, find the mean and standard deviation.
Sol: Given, n = 18, Σ (x – 5) = 3 and Σ (x – 5)2 = 43
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 20

Q15. Find the mean and variance of the frequency distribution given below:
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 21
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 22

Long Answer Type Questions
Q16. Calculate the mean deviation about the mean for the following frequency distribution:

Class interval 0-4 4-8 8-12 12-16 16-20
Frequency 4 6 8 5 2

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 23

Q17. Calculate the mean deviation from the median of the following data

Class interval 0 – 6 6 – 12 12 -18 18 -24 24 -30
Frequency 4 5 3 6 2

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 24
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 25

Q18. Determine the mean and standard deviation for the following distribution:

Marks 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Frequency 1 6 6 8 8 2 2 3 0 2 1 0 0 0 1

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 26
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 27

Q19. The weights of coffee in 70 jars are shown in the following table:

Weight (in grams) Frequency
200-201 13
201-202 27
202 – 203 18
203-204 10
204-205 1
205-206 1

Determine variance and standard deviation of the above distribution.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 28
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 29

Q20. Determine mean and standard deviation of first n terms of an A.P. whose first term is a and common difference is d.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 30
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 31

Q21. Following are the marks obtained, out of 100, by two students Ravi and Hashinain 10 tests.

Ravi 25 50 45 30 70 42 36 48 35 60
Hashina 10 70 50 20 95 55 42 60 48 80

Who is more intelligent and who is more consistent?
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 32
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 33
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 34
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 35

Q22. Mean and standard deviation of 100 observations were found to be 40 and 10,respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 36

Q23. While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 37
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 38
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 39

Objective Type Questions
Q24. The mean deviation of the data 3,10, 10,4, 7, 10, 5 from the mean is (a) 2 (b) 2.57 (c) 3 (d) 3.75
Sol: (b) Given, observations are 3, 10, 10, 4, 7, 10 and 5.
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 40
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 41

Q26. When tested, the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623 The mean deviations (in hours) from their mean is (a) 178 (b) 179 (c) 220 (d) 356
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 42

Q27. Following are the marks obtained by 9 students in a mathematics test:
50, 69,20, 33, 53, 39,40, 65, 59 The mean deviation from the median is:
(a) 9 (b) 10.5 (c) 12.67 (d) 14.76
Sol: (c) Since, marks obtained by 9 students in Mathematics are 50,69,20,33,53, 39,40, 65 and 59.
Rewrite the given data in ascending order.
20, 33, 39,40, 50, 53, 59, 65, 69,
Here, n = 9 [odd]

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 43
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 44
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 45
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 46

Q30. The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is
(a) 50000 (b) 250000 (c) 252500 (d) 255000
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 47

Q31. Let a, b, c, d, e be the observations with mean m and standard deviation V. The standard deviation of the observations a + k,b + k,c + k,d+k,e + k is
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 48
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 49
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 50
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 51

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 52
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 53

Q34. Standard deviations for first 10 natural numbers is
(a) 5.5 (b) 3.87 (c) 2.97 (d) 2.87

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 54

Q35. Consider the numbers 1,2, 3,4, 5, 6, 7, 8,9,10. If 1 is added to each number, the variance of the numbers so obtained is
(a) 6.5 (b) 2.87 (c) 3.87 (d) 8.25
Sol: (d) Given numbers are 1, 2, 3,4, 5, 6, 7, 8, 9 and 10
If 1 is added to each number, then observations will be 2, 3,4, 5, 6,7, 8, 9, 10 and 11.

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 55

Q36. Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is (a) 8.25 (b) 6.5 (c) 3.87 (d) 2.87
Sol: 
(a) Since, the first 10 positive integers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.
On multiplying each number by -1, we get
-1, -2, -3, -4, -5, -6, -7, -8, -9, -10 On adding 1 in each number, we get
0, -1, -2, -3, -4, -5, -6, -7, -8, -9

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 56
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 57
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 58

Q38. Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is
(a) 0 (b) 1 (c) 1.5 (d) 2.5
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 59

Q39. The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be
(a) 81 (b) 57 (c) 36 (d) 25
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 60

Fill in the Blanks
NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 61

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 62

NCERT Exemplar Class 11 Maths Chapter 15 Statistics Img 63

Q43. The standard deviation of a data is _____ of any change in origin, but is ________ on the change of scale.
Sol: The standard deviation of a data is independent of any change in origin but is dependent of charge of scale.
Q44. The sum of the squares of the deviations of the values of the variable is ________ when taken about their arithmetic mean.
Sol: The sum of the squares of the deviations of the values of the variable is minimum when taken about their arithmetic mean.
Q45. The mean deviation of the data is ________ when measured from the median.
Sol: The mean deviation of the data is least when measured from the median.
Q46. The standard deviation is________ to the mean deviation taken from the arithmetic mean.
Sol: The standard deviation is greater than or equal to the mean deviation taken from the arithmetic mean.

NCERT Exemplar Class 11 Maths Solutions

  • 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 Permutations and Combinations
  • Chapter 8 Binomial Theorem
  • Chapter 9 Sequence 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

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