English

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 - Mathematics

Advertisements
Advertisements

Question

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

Advertisements

Solution

Let the observations be x1x2x3x4x5, and x6.

It is given that mean is 8 and standard deviation is 4.

shaalaa.com
  Is there an error in this question or solution?

RELATED QUESTIONS

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 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 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12 and 14. 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:

  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:

 2, 4, 5, 6, 8, 17.


Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.


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


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.


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 standard deviation for the following data:

Class: 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequency: 9 17 43 82 81 44 24

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?

 

 


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 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 the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write the value of standard deviation.

 

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.
 
 

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 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


The standard deviation of first 10 natural numbers is


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 ______.


Find the standard deviation of the first n natural numbers.


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.


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.


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.


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 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, ... 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 ______.


Standard deviations for first 10 natural numbers is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×