Class 11 Maths Chapter 13 Statistics

NCERT Solutions of Class 11 Maths Chapter 13 Statistics

Exercise 13.1

Find the mean deviation about the mean for the data in Exercises 1 and 2.
1. 4, 7, 8, 9, 10, 12, 13, 17
2. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

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Find the mean deviation about the median for the data in Exercises 3 and 4.
3. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
4. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Find the mean deviation about the mean for the data in Exercises 5 and 6.
5.   x_i 5   10   15   20   25
       f_i 7     4     6     3     5
6.   x_i 10   30   50   70   90
      f_i 4     24    28     16     8

Find the mean deviation about the median for the data in Exercises 7 and 8.
7.   x_i 5   7   9   10   12 15
      f_i  8   6   2    2   2 6
8.   x_i 15   21   27   30   35
      f_i 3     5    6     7     8

Find the mean deviation about the mean for the data in Exercises 9 and 10.
9.

10.

11. Find the mean deviation about median for the following data :

12. Calculate the mean deviation about median age for the age distribution of 100 persons given below:

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NCERT Solutions of Class 11 Maths Chapter 13 Statistics

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Exercise 13.2

Find the mean and variance for each of the data in questions 1 to 5.
1. 6, 7, 10, 12, 13, 4, 8, 12
2. First n natural numbers
3. First 10 multiples of 3
4.

5.

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NCERT Solutions of Class 11 Maths Chapter 13 Statistics

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6. Find the mean and standard deviation using short-cut method.

Find the mean and variance for the following frequency distributions in Exercises 7 and 8.
7.

8.

9. Find the mean, variance and standard deviation using short-cut method.

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

Calculate the standard deviation and mean diameter of the circles.

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NCERT Solutions of Class 11 Maths Chapter 13 Statistics

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Miscellaneous Exercise on Chapter 13

Question 1:
The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

Question 2:
The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

Question 3:
The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations

Question 4:
Given that x̄ is the mean and σ² is the variance of n observations x₁, x₂, …,x_n. Prove that the mean and variance of the observations ax₁, ax₂, ax₃, …., ax_n are a x̄ and a² σ², respectively, (a ≠ 0).

Question 5:
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect.
Calculate the correct mean and standard deviation in each of the following cases:
(i) If wrong item is omitted. (ii) If it is replaced by 12.

Question 6:
The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

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NCERT Solutions of Class 11 Maths Chapter 13 Statistics

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