मराठी

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

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प्रश्न

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

रिकाम्या जागा भरा

उत्तर

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

Explanation:

Since the standard deviation of any data is independent of any change in origin but is dependent of any change of scale.

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पाठ 15: Statistics - Exercise [पृष्ठ २८३]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 15 Statistics
Exercise | Q 43 | पृष्ठ २८३

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.


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


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.


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

 2, 4, 5, 6, 8, 17.


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

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


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.


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.

 

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.

 

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.


Find the standard deviation for the following data:

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

Find the mean and variance of frequency distribution given below:

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

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.      


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 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 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.

 

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

 


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


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

`sigma = sqrt((x_i - barx)^2/n)` and `sigma`' = `sqrt((x^2_i)/n - barx^2)` are equivalent.


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?


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 seconds. Further, another set of 15 observations x1, x2, ..., x15, also in seconds, is now available and we have `sum_(i = 1)^15 x_i` = 279 and `sum_(i  = 1)^15 x^2` = 5524. Calculate the standard derivation based on all 40 observations.


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.


The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is ______.


Let x1, x2, ..., xn be n observations and `barx` be their arithmetic mean. The formula for the standard deviation is given by ______.


Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is ______.


Standard deviations for first 10 natural numbers is ______.


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 ______.


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


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