मराठी

Standard deviations for first 10 natural numbers is ______.

Advertisements
Advertisements

प्रश्न

Standard deviations for first 10 natural numbers is ______.

पर्याय

  • 5.5

  • 3.87

  • 2.97

  • 2.87

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

Standard deviations for first 10 natural numbers is 2.87.

Explanation:

We know that S.D. of first n natural numbers `sqrt((n^2 - 1)/12)`

Here n = 10

∴ S.D. = `sqrt((10)^2 - 1)/12`

= `sqrt(99/12)`

= `sqrt(8.25)`

= 2.87

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 15: Statistics - Exercise [पृष्ठ २८२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 15 Statistics
Exercise | Q 34 | पृष्ठ २८२

संबंधित प्रश्‍न

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


Find the mean and variance for the data.

xi 6 10 14 18 24 28 30
fi 2 4 7 12 8 4 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 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.


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 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 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

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

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.      


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?


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.

 

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.


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

 


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


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.


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 ______.


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 ______.


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 ______.


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


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


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×