English

Standard deviations for first 10 natural numbers is ______.

Advertisements
Advertisements

Question

Standard deviations for first 10 natural numbers is ______.

Options

  • 5.5

  • 3.87

  • 2.97

  • 2.87

MCQ
Fill in the Blanks
Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 15: Statistics - Exercise [Page 282]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 15 Statistics
Exercise | Q 34 | Page 282

RELATED QUESTIONS

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 data.

xi 6 10 14 18 24 28 30
fi 2 4 7 12 8 4 3

Find the mean and variance for the data.

xi 92 93 97 98 102 104 109
fi 3 2 3 2 6 3 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 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 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


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 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:

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.


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 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:
(i) If wrong item is omitted
(ii) if it is replaced by 12.


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.


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

\[\sigma = \sqrt{\frac{1}{n} \sum \left( x_i - X \right)^2_{}}\] and 

\[\sigma' = \sqrt{\frac{1}{n} \sum x_i^2 - X^2_{}}\]  are equivalent, where \[X = \frac{1}{n}\sum_{} x_i\]

 

 

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

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 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?

 

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

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.

 

The standard deviation of the data:

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

is


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

 

The standard deviation of first 10 natural numbers 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 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.


If for distribution `sum(x - 5)` = 3, `sum(x - 5)^2` = 43 and total number of items is 18. Find the mean and 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 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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×