मराठी

The standard deviation is ______to the mean deviation taken from the arithmetic mean. - Mathematics

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प्रश्न

The standard deviation is ______to the mean deviation taken from the arithmetic mean.

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उत्तर

The standard deviation is greater than or equal to the mean deviation taken from the arithmetic mean.

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पाठ 15: Statistics - Exercise [पृष्ठ २३८]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 15 Statistics
Exercise | Q 46 | पृष्ठ २३८

संबंधित प्रश्‍न

Find the mean and variance for the data.

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


Find the mean and variance for the first n natural numbers.


Find the mean and variance for the first 10 multiples of 3.


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

No. of goals scored

0

1

2

3

4

No. of matches

1

9

7

5

3

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


The sum and sum of squares corresponding to length (in cm) and weight (in gm) of 50 plant products are given below:

`sum_(i-1)^50 x_i = 212, sum_(i=1)^50 x_i^2 = 902.8, sum_(i=1)^50 y_i = 261, sum_(i = 1)^50 y_i^2 = 1457.6`

Which is more varying, the length or weight?

 

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.


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?


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

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


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

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


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

 

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.

 

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?


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

Find the standard deviation for the following data:

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

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.


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.  


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?

 

 


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?

 

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.

 

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.
 
 

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


The standard deviation of first 10 natural numbers is


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


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 

 
 
 
   

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


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

Length of life
(in hours)
Factory A
(Number of bulbs)
Factory B
(Number of bulbs)
550 – 650 10 8
650 – 750 22 60
750 – 850 52 24
850 – 950 20 16
950 – 1050 16 12
  120 120

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


A set of n values x1, x2, ..., xn has standard deviation 6. The standard deviation of n values x1 + k, x2 + k, ..., xn + k will be ______.


The mean and standard deviation of a set of n1 observations are `barx_1` and s1, respectively while the mean and standard deviation of another set of n2 observations are `barx_2` and  s2, respectively. Show that the standard deviation of the combined set of (n1 + n2) observations is given by

S.D. = `sqrt((n_1(s_1)^2 + n_2(s_2)^2)/(n_1 + n_2) + (n_1n_2 (barx_1 - barx_2)^2)/(n_1 + n_2)^2)`


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.


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.


Let x1, x2, ... xn be n observations. Let wi = lxi + k for i = 1, 2, ...n, where l and k are constants. If the mean of xi’s is 48 and their standard deviation is 12, the mean of wi’s is 55 and standard deviation of wi’s is 15, the values of l and k should be ______.


Standard deviations for first 10 natural numbers is ______.


If the variance of a data is 121, then the standard deviation of the data is ______.


The standard deviation of a data is ______ of any change in orgin, but is ______ on the change of scale.


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.


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