मराठी

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

Advertisements
Advertisements

प्रश्न

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

रिकाम्या जागा भरा
Advertisements

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.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 15: Statistics - Exercise [पृष्ठ २८३]

APPEARS IN

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

Diameters 33 - 36 37 - 40 41 - 44 45 - 48 49 - 52
No. of circles 15 17 21 22 25

Calculate the standard deviation and mean diameter of the circles.

[Hint: First make the data continuous by making the classes as 32.5 - 36.5, 36.5 - 40.5, 40.5 - 44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]


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.


Given that  `barx` is the mean and σ2 is the variance of n observations x1, x2, …,xn. Prove that the mean and variance of the observations ax1, ax2, ax3, …,axare `abarx` and a2 σ2, respectively (a ≠ 0).


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

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

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

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

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.  


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?

 

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


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?

 

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

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

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.
 
 

The standard deviation of the data:

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

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 

 
 
 
   

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.


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.


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 and `barx` be their arithmetic mean. The formula for the standard deviation is given by ______.


Let x1, x2, x3, x4, x5 be the observations with mean m and standard deviation s. The standard deviation of the observations kx1, kx2, kx3, kx4, kx5 is ______.


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


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×