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RD Sharma solutions for Class 11 Mathematics chapter 32 - Statistics

Mathematics Class 11

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Chapters

RD Sharma Mathematics Class 11

Mathematics Class 11

Chapter 32 : Statistics

Page 6

Q 1.1 | Page 6

Calculate the mean deviation about the median of the observation:

3011, 2780, 3020, 2354, 3541, 4150, 5000

Q 1.2 | Page 6

Calculate the mean deviation about the median of the observation:

 38, 70, 48, 34, 42, 55, 63, 46, 54, 44

Q 1.3 | Page 6

Calculate the mean deviation about the median of the observation:

 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

Q 1.4 | Page 6

Calculate the mean deviation about the median of the observation:

 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

Q 1.5 | Page 6

Calculate the mean deviation about the median of the observation:

 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

 
Q 2.1 | Page 6

Calculate the mean deviation from the mean for the data: 

 4, 7, 8, 9, 10, 12, 13, 17

Q 2.2 | Page 6

Calculate the mean deviation from the mean for the  data:

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

Q 2.3 | Page 6

Calculate the mean deviation from the mean for the  data:

 38, 70, 48, 40, 42, 55, 63, 46, 54, 44a

Q 2.4 | Page 6

Calculate the mean deviation from the mean for the  data:

(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

 
Q 3 | Page 6

Calculate the mean deviation of the following income groups of five and seven members from their medians:

I
Income in Rs.
II
Income in Rs.
4000
4200
4400
4600
4800

 
 300
4000
4200
4400
4600
4800
5800
Q 4.1 | Page 6

The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2
 Find mean deviation from median

Q 4.2 | Page 6

The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2 

Find mean deviation from the mean also.

 

 

Q 5.1 | Page 6

In 34, 66, 30, 38, 44, 50, 40, 60, 42, 51 find the number of observations lying between

\[\bar{ X } \]  − M.D. and

\[\bar{ X } \]  + M.D, where M.D. is the mean deviation from the mean.

Q 5.2 | Page 6

In  22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between 

\[\bar { X } \]  − M.D. and

\[\bar { X } \]   + M.D, where M.D. is the mean deviation from the mean.

Q 5.3 | Page 6

In 38, 70, 48, 34, 63, 42, 55, 44, 53, 47 find the number of observations lying between

\[\bar { X } \]  − M.D. and

\[\bar { X } \]   + M.D, where M.D. is the mean deviation from the mean.

Page 11

Q 1 | Page 11

Calculate the mean deviation from the median of the following frequency distribution:

Heights in inches 58 59 60 61 62 63 64 65 66
No. of students 15 20 32 35 35 22 20 10 8
Q 2 | Page 11

The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution:

Number of calls 0 1 2 3 4 5 6 7
Frequency 14 21 25 43 51 40 39 12

Compute the mean deviation about median.

Q 3 | Page 11

Calculate the mean deviation about the median of the following frequency distribution:

xi 5 7 9 11 13 15 17
fi 2 4 6 8 10 12 8
Q 4.1 | Page 11

Find the mean deviation from the mean for the data:

xi 5 7 9 10 12 15
fi 8 6 2 2 2 6
Q 4.2 | Page 11

Find the mean deviation from the mean for the data:

xi 5 10 15 20 25
fi 7 4 6 3 5
Q 4.3 | Page 11

Find the mean deviation from the mean for the data:

xi 10 30 50 70 90
fi 4 24 28 16 8
Q 4.4 | Page 11

Find the mean deviation from the mean for the data:

Size 20 21 22 23 24
Frequency 6 4 5 1 4
Q 4.5 | Page 11

Find the mean deviation from the mean for the data:

Size 1 3 5 7 9 11 13 15
Frequency 3 3 4 14 7 4 3 4
Q 5.1 | Page 11

Find the mean deviation from the median for the  data:

xi 15 21 27 30 35
fi 3 5 6 7 8

 

Q 5.2 | Page 11

Find the mean deviation from the median for the  data: 

xi 74 89 42 54 91 94 35
fi 20 12 2 4 5 3 4

Pages 16 - 17

Q 1 | Page 16

Compute the mean deviation from the median of the following distribution:

Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 10 20 5 10
Q 2.1 | Page 16

Find the mean deviation from the mean for the data:

Classes 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800
Frequencies 4 8 9 10 7 5 4 3

 

Q 2.2 | Page 16

Find the mean deviation from the mean for the data:

Classes 95-105 105-115 115-125 125-135 135-145 145-155
Frequencies 9 13 16 26 30 12

 

Q 2.3 | Page 16

Find the mean deviation from the mean for the data:

Classes 0-10 10-20 20-30 30-40 40-50 50-60
Frequencies 6 8 14 16 4 2
Q 3 | Page 16

Compute mean deviation from mean of the following distribution:

Mark 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
No. of students 8 10 15 25 20 18 9 5
Q 4 | Page 16

The age distribution of 100 life-insurance policy holders is as follows:

Age (on nearest birth day) 17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5
No. of persons 5 16 12 26 14 12 6 5

Calculate the mean deviation from the median age

Q 5 | Page 16

Find the mean deviation from the mean and from median of the following distribution:

Marks 0-10 10-20 20-30 30-40 40-50
No. of students 5 8 15 16 6
Q 6 | Page 16

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

Age: 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55
Number of persons 5 6 12 14 26 12 16 9
Q 7 | Page 17

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
Q 8 | Page 17

Calculate 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

Page 28

Q 1.1 | Page 28

Find the mean, variance and standard deviation for the data:

 2, 4, 5, 6, 8, 17.

Q 1.2 | Page 28

Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.

Q 1.3 | Page 28

Find the mean, variance and standard deviation for the data:

 227, 235, 255, 269, 292, 299, 312, 321, 333, 348.

Q 1.4 | Page 28

Find the mean, variance and standard deviation for the data 15, 22, 27, 11, 9, 21, 14, 9.

 
Q 2 | Page 28

The variance of 20 observations is 5. If each observation is multiplied by 2, find the variance of the resulting observations.

 
Q 3 | Page 28

The variance of 15 observations is 4. If each observation is increased by 9, find the variance of the resulting observations.

Q 4 | Page 28

The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.

 
Q 5 | Page 28

The mean and standard deviation of 6 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.

Q 6 | Page 28

The mean and variance of 8 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.

 
Q 7 | Page 28

For a group of 200 candidates, the mean and standard deviations of scores were found to be 40 and 15 respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53 respectively. Find the correct mean and standard deviation.

 
Q 8 | Page 28

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?

Q 9 | Page 28

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.

Q 10 | Page 28

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 were omitted.

Q 11 | Page 28

Show that the two formulae for the standard deviation of ungrouped data 

\[\sigma = \sqrt{\frac{1}{n} \sum \left( x_i - X \right)^2_{}}\] and 

\[\sigma' = \sqrt{\frac{1}{n} \sum x_i^2 - X^2_{}}\]  are equivalent, where \[X = \frac{1}{n}\sum_{} x_i\]

 

 

Pages 37 - 38

Q 1 | Page 37

Find the standard deviation for the following distribution:

x : 4.5 14.5 24.5 34.5 44.5 54.5 64.5
f : 1 5 12 22 17 9 4
Q 2 | Page 38

Table below shows the frequency f with which 'x' alpha particles were radiated from a diskette 

x : 0 1 2 3 4 5 6 7 8 9 10 11 12
f : 51 203 383 525 532 408 273 139 43 27 10 4 2

Calculate the mean and variance.

 

 
Q 3 | Page 38

Find the mean, mode, S.D. and coefficient of skewness for the following data: 

Year render: 10 20 30 40 50 60
No. of persons (cumulative): 15 32 51 78 97 109
Q 4 | Page 38

Find the standard deviation for the following data:

x : 3 8 13 18 23
f : 7 10 15 10 6

Pages 0 - 42

Calculate the mean and S.D. for the following data:

Expenditure in Rs: 0-10 10-20 20-30 30-40 40-50
Frequency: 14 13 27 21 15

Calculate the standard deviation for the following data:

Class: 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequency: 9 17 43 82 81 44 24

Calculate the A.M. and S.D. for the following distribution:

Class: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency: 18 16 15 12 10 5 2 1

A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and S.D.

Calculate the mean, median and standard deviation of the following distribution:

Class-interval: 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70
Frequency: 2 3 8 12 16 5 2 3

Find the mean and variance of frequency distribution given below:

xi: 1 ≤ < 3 3 ≤ < 5 5 ≤ < 7 7 ≤ < 10
fi: 6 4 5 1

The weight of coffee in 70 jars is shown in the following table:                                                  

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

Determine the variance and standard deviation of the above distribution.  

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.      

While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Calculate the mean, variance and standard deviation of the following frequency distribution. 

Class: 1–10 10–20 20–30 30–40 40–50 50–60
Frequency: 11 29 18 4 5 3

Pages 47 - 49

Q 1 | Page 47

Two plants A and B of a factory show following results about the number of workers and the wages paid to them 

  Plant A Plant B
No. of workers 5000 6000
Average monthly wages Rs 2500 Rs 2500
Variance of distribution of wages 81 100

In which plant A or B is there greater variability in individual wages?

 

 

Q 2 | Page 47

The means and standard deviations of heights ans weights of 50 students of a class are as follows: 

  Weights Heights
Mean 63.2 kg 63.2 inch
Standard deviation 5.6 kg 11.5 inch

Which shows more variability, heights or weights?

 
Q 3 | Page 48

Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

Q 4 | Page 48

Calculate coefficient of variation from the following data:

Income (in Rs): 1000-1700 1700-2400 2400-3100 3100-3800 3800-4500 4500-5200
No. of families: 12 18 20 25 35 10
Q 5 | Page 48

An analysis of the weekly 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
Average weekly wages Rs 52.5 Rs. 47.5
Variance of the

100
 
121
distribution of wages    

(i) Which firm A or B pays out larger amount as weekly wages?
(ii) Which firm A or B has greater variability in individual wages?

Q 6 | Page 48

The following are some particulars of the distribution of weights of boys and girls in a class: 

Number Boys Girls
  100 50
Mean weight 60 kg 45 kg
Variance 9 4

Which of the distributions is more variable?

 
Q 7 | Page 48

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below: 

Subject Mathematics Physics Chemistry
Mean 42 32 40.9
Standard Deviation 12 15 20

Which of the three subjects shows the highest variability in marks and which shows the lowest?

 
Q 8 | Page 48

From the data given below state which group is more variable, G1 or G2?

Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group G1 9 17 32 33 40 10 9
Group G2 10 20 30 25 43 15 7
Q 9 | Page 48

Find the coefficient of variation for the following data:

Size (in cms): 10-15 15-20 20-25 25-30 30-35 35-40
No. of items: 2 8 20 35 20 15
Q 10 | Page 48

From the prices of shares X and Y given 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
Q 11 | Page 49

Life of bulbs produced by two factories A and B are given below:

Length of life
(in hours):
550–650 650–750 750–850 850–950 950–1050

Factory A:
(Number of bulbs)
 
10 22 52 20 16

Factory B:
(Number of bulbs)
 
8 60 24 16 12

The bulbs of which factory are more consistent from the point of view of length of life?  

 

Q 12 | Page 49

Following are the marks obtained,out of 100 by two students Ravi and Hashina in 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? 

Page 49

Q 1 | Page 49

Write the variance of first n natural numbers.

 
Q 2 | Page 49

If the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write the value of standard deviation.

 
Q 3 | Page 49

If x1x2, ..., xn are n values of a variable X and y1y2, ..., yn are n values of variable Y such that yi = axi + bi = 1, 2, ..., n, then write Var(Y) in terms of Var(X).

 
Q 4 | Page 49

If X and Y are two variates connected by the relation

\[Y = \frac{aX + b}{c}\]  and Var (X) = σ2, then write the expression for the standard deviation of Y.
 
 
Q 5 | Page 49

In a series of 20 observations, 10 observations are each equal to k and each of the remaining half is equal to − k. If the standard deviation of the observations is 2, then write the value of k.

Q 6 | Page 49

If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.

 
Q 7 | Page 49

If a variable X takes values 0, 1, 2,..., n with frequencies nC0nC1nC2 , ... , nCn, then write variance X.

Pages 50 - 52

Q 1 | Page 50

For a frequency distribution mean deviation from mean is computed by

M.D. = \[\frac{\Sigma f}{\Sigma f \left| d \right|}\]

 

M.D. = \[\frac{\Sigma d}{\Sigma f}\]

 

 M.D. = \[\frac{\Sigma f d}{\Sigma f}\]

 

M.D. = \[\frac{\Sigma f \left| d \right|}{\Sigma f}\]

 
Q 2 | Page 50

For a frequency distribution standard deviation is computed by applying the formula

\[\sigma = \sqrt{\frac{\Sigma f d^2}{\Sigma f} - \left( \frac{\Sigma f d}{\Sigma f} \right)^2}\]

 

 \[\sigma = \sqrt{\left( \frac{\Sigma f d}{\Sigma f} \right)^2 - \frac{\Sigma f d^2}{\Sigma f}}\]

 

\[\sigma = \sqrt{\frac{\Sigma f d^2}{\Sigma f} - \frac{\Sigma fd}{\Sigma f}}\]

 

\[\sqrt{\left( \frac{\Sigma fd}{\Sigma f} \right)^2 - \frac{\Sigma f d^2}{\Sigma f}}\]

 

Q 3 | Page 50

If v is the variance and σ is the standard deviation, then

 

\[v = \frac{1}{\sigma^2}\]

  

 \[v = \frac{1}{\sigma}\]

 

 v = σ2

 v2 = σ

 
Q 4 | Page 50

The mean deviation from the median is

 equal to that measured from another value

 maximum if all observations are positive

 greater than that measured from any other value.

less than that measured from any other value.

 
Q 5 | Page 50

If n = 10, \[X = 12\]   and \[\Sigma x_i^2 = 1530\] , then the coefficient of variation is

  

36%

41%

 25%

none of these

 
Q 6 | Page 50

The standard deviation of the data:

x: 1 a a2 .... an
f: nC0 nC1 nC2 .... nCn

is

\[\left( \frac{1 + a^2}{2} \right)^n - \left( \frac{1 + a}{2} \right)^n\]

 

 \[\left( \frac{1 + a^2}{2} \right)^{2n} - \left( \frac{1 + a}{2} \right)^n\]

 \[\left( \frac{1 + a}{2} \right)^{2n} - \left( \frac{1 + a^2}{2} \right)^n\]

 

none of these

 
Q 7 | Page 50

The mean deviation of the series aa + da + 2d, ..., a + 2n from its mean is

 \[\frac{(n + 1) d}{2n + 1}\]

 

\[\frac{nd}{2n + 1}\]

 

 \[\frac{n (n + 1) d}{2n + 1}\]

 

\[\frac{(2n + 1) d}{n (n + 1)}\]

 
Q 8 | Page 50

A batsman scores runs in 10 innings as 38, 70, 48, 34, 42, 55, 63, 46, 54 and 44. The mean deviation about mean is

 8.6

 6.4

10.6

7.6

 

  None of these

Q 9 | Page 51

The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is

25

 5

1.2

0

 
Q 10 | Page 51

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

10 %

40 %

 50 %

none of these

 
Q 11 | Page 51

Let x1x2, ..., xn be values taken by a variable X and y1y2, ..., yn be the values taken by a variable Y such that yi = axi + bi = 1, 2,..., n. Then,

Var (Y) = a2 Var (X)

Var (X) = a2 Var (Y)

 Var (X) = Var (X) + b

none of these

 
Q 12 | Page 51

If the standard deviation of a variable X is σ, then the standard deviation of variable \[\frac{a X + b}{c}\] is

 

a σ

 \[\frac{a}{c}\sigma\]

 

\[\left| \frac{a}{c} \right| \sigma\]

 \[\frac{a\sigma + b}{c}\]

Q 13 | Page 51

If the S.D. of a set of observations is 8 and if each observation is divided by −2, the S.D. of the new set of observations will be

−4

−8

8

 4

 
Q 14 | Page 51

If two variates X and Y are connected by the relation \[Y = \frac{a X + b}{c}\] , where abc are constants such that ac < 0, then

 

  \[\sigma_Y = \frac{a}{c} \sigma_X\]

\[\sigma_Y = - \frac{a}{c} \sigma_X\]

 \[\sigma_Y = \frac{a}{c} \sigma_X + b\]

none of these

 
Q 15 | Page 51

If for a sample of size 60, we have the following information \[\sum_{} x_i^2 = 18000\] and \[ \sum_{} x_i = 960 \] , then the variance is

 

6.63   

 16  

22    

44 

Q 16 | Page 51

Let abcdbe the observations with mean m and standard deviation s. The standard deviation of the observations a + kb + kc + kd + ke + k is

s     

ks    

 s + k    

\[\frac{s}{k}\]

Q 17 | Page 51

The standard deviation of first 10 natural numbers is

 5.5   

3.87 

2.97   

2.87 

Q 18 | Page 51

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

 8.25  

6.5       

3.87 

2.87 

Q 19 | Page 51

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

 6.5  

2.87   

 3.87  

8.25 

Q 20 | Page 51

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is 

 50,000 

 250,000  

252500 

255000          

Q 21 | Page 51

Let x1x2, ..., xn be n observations. Let  \[y_i = a x_i + b\]  for i = 1, 2, 3, ..., n, where a and b are constants. If the mean of \[x_i 's\]  is 48 and their standard deviation is 12, the mean of \[y_i 's\]  is 55 and standard deviation of \[y_i 's\]  is 15, the values of a and are 

 
 
 
   

a = 1.25, b = −5 

a = −1.25, b = 5

 a = 2.5, b = −5  

 a = 2.5, b = 5 

Q 22 | Page 51

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is

2    

 2.57       

 3        

 3.57 

Q 23 | Page 52

The mean deviation for n observations \[x_1 , x_2 , . . . , x_n\]  from their mean \[\bar{X} \]  is given by

 
  

 \[\sum^n_{i = 1} \left( x_i - X \right)\]

\[\frac{1}{n} \sum^n_{i = 1} \left( x_i - X \right)\]

 

  \[\sum^n_{i = 1} \left( x_i - X \right)^2\]

  \[\frac{1}{n} \sum^n_{i = 1} \left( x_i - X \right)^2\]

Q 24 | Page 52

Let \[x_1 , x_2 , . . . , x_n\]  be n observations and  \[X\]  be their arithmetic mean. The standard deviation is given by

 

\[\sum^n_{i = 1} \left( x_i - X \right)^2\]

 \[\frac{1}{n}\sum^n_{i = 1}\left( x_i - X \right)^2\]

\[\sqrt{\frac{1}{n} \sum^n_{i = 1} \left( x_i - X \right)^2}\]

 \[\sqrt{\frac{1}{n} \sum^n_{i = 1} x_i^2 - X^2}\]

Q 25 | Page 52

The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is

\[\sqrt{6}\]

  \[\frac{52}{7}\]

 \[\sqrt{\frac{52}{7}}\]

RD Sharma Mathematics Class 11

Mathematics Class 11

RD Sharma solutions for Class 11 Mathematics chapter 32 - Statistics

RD Sharma solutions for Class 11 Maths chapter 32 (Statistics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 32 Statistics are Standard Deviation - by Short Cut Method, Measures of Dispersion - Quartile Deviation, Central Tendency - Mode, Central Tendency - Mean, Statistics Concept, Comparison of Two Frequency Distributions with Same Mean, Introduction of Analysis of Frequency Distributions, Shortcut Method to Find Variance and Standard Deviation, Standard Deviation of a Continuous Frequency Distribution, Standard Deviation of a Discrete Frequency Distribution, Standard Deviation, Introduction of Variance and Standard Deviation, Mean Deviation, Concept of Range, Measures of Dispersion, Central Tendency - Median.

Using RD Sharma Class 11 solutions Statistics exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

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