Home
Class 12
MATHS
Let a, b, c, d, e, be the observations w...

Let a, b, c, d, e, be the observations with m and standard deviation s. The standard deviation of the observations a+k, b+k, c+k, d+k, e+k is (a) `s` (b) `k s` (c) `s+k` (d) `s/k`

A

s

B

ks

C

s+k

D

`(s)/(k)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given observations are a, b, c, d and e.
Mean `=m=(a+b+c+d+e)/(5)`
`sum x_(i)=a+b+c+d+e=5 m`
New mean `=(a+k+b+k+c+k+d+k+e+k)/(5)`
`=((a+b+c+d+e)+5k)/(5)=m+k`
`therefore S.D. =sqrt((sum(x_(i)^(2)+k^(2)+2kx_(i)))/(n)-(m^(2)+k^(2)+2mk))`
`=sqrt((sum x_(i)^(2))/(n)-m^(2)+(2k sum x_(i))/(n)-2mk)`
`=sqrt((sum x_(i)^(2))/(n)-m^(2)+2km-2mk)" " [because (sum x_(i))/(n)=m]`
`=sqrt((sum x_(i)^(2))/(n)-m^(2))`
=s
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    CENGAGE ENGLISH|Exercise Exercise 11.1|5 Videos

  • STATISTICS

    CENGAGE ENGLISH|Exercise Exercise 11.2|6 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

  • STRAIGHT LINE

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|8 Videos

Similar Questions

Explore conceptually related problems

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 (a) s (b) k s (c) s+k (d) s/k

Let a, b, c, d, e, be the observations with m and standard deviation s. The standard deviation of the observations a+k, b+k, c+k, d+k, e+k is s (b) k s (c) s+k (d) s/k

The mean of 40 observations 20 and their standard deviation is 5. If the sum of the square of the observations k, then the value of (k)/(1000) is

The mean of n observations is X dot If each observation is multiplied by k , the mean of new observation is k X (b) ( X )/k (c) X +k (d) X -k

A set of n values x_(1),x_(2),…….,x_(n) has standard deviation sigma . The standard deviation of n values x_(1)-k,x_(2)-k,…….,x_(n)-k is

The mean of n observations is xdot If k is added to each observation, then the new mean is X (b) X +k (c) X -k (d) k X

Let s be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation of the resulting number is

In a series of 20 observations, 10 observation 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 A=[a b c d] (where b c!=0 ) satisfies the equations x^2+k=0,t h e n a+d=0 b. K=-|A| c. k=|A| d. none of these

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.