हिंदी

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.

Advertisements
Advertisements

प्रश्न

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.

 
Advertisements

उत्तर

The sum of the squares of deviations for 10 observations, taken from their mean, is 2.5. 
Square of each deviation =  \[\frac{2 . 5}{10} = 0 . 25\]

Standard deviation = \[\sqrt{0 . 25} = 0 . 5\]

 
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 32: Statistics - Exercise 32.8 [पृष्ठ ४९]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 32 Statistics
Exercise 32.8 | Q 2 | पृष्ठ ४९

संबंधित प्रश्न

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 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).


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:

  1. If wrong item is omitted.
  2. If it is replaced by 12.

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:

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


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.


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 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 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

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?

 

 


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.
 
 

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

 


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

 

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


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.


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?


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.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×