हिंदी

A set of n values x1, x2, ..., x n has standard deviation 6. The standard deviation of n values x1 + k, x2 + k, ..., xn + k will be ______.

Advertisements
Advertisements

प्रश्न

A set of n values x1, x2, ..., xn has standard deviation 6. The standard deviation of n values x1 + k, x2 + k, ..., xn + k will be ______.

विकल्प

  • σ

  • σ + k

  • σ – k

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

A set of n values x1, x2, ..., xn has standard deviation 6. The standard deviation of n values x1 + k, x2 + k, ..., xn + k will be σ.

Explanation:

If each observation is increased by a constant k

Then standard deviation is unchanged.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 15: Statistics - Solved Examples [पृष्ठ २७७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 15 Statistics
Solved Examples | Q 9 | पृष्ठ २७७

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

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

 

The variance of 15 observations is 4. If each observation is increased by 9, 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.

 

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

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.  


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?

 

 


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 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 mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is 


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)`


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 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 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 ______.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×