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

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|Exercise Exercise 11.1|5 Videos

  • STATISTICS

    CENGAGE|Exercise Exercise 11.2|6 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

Similar Questions

Explore conceptually related problems

Standard deviation of four observations -1,0,1 and k is sqrt(5) then k will be

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

If mean of squares of deviations of a set of n observations about -2 and 2 are 18 and 10 respectively then standard deviation of this set of observations is 3 (b) 2 (c) 1 (d) None of these

a+2 , b+2 , c+2 are 3 observations such that b=a+c , and a+2 , b+2 , c+2 has standard deviation = d Then

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

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

If standard deviation of a set of observation is 4 and if each of the observations is divided by 4, then the standard deviation of new set of observations is