JEE Exam > JEE Questions > The mean and the standard deviation (s.d.) of...
Start Learning for Free
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal to
- a)-10
- b)-20
- c)-5
- d)10
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The mean and the standard deviation (s.d.) of 10 observations are 20 a...
Let's assume the 10 observations are denoted by x1, x2, ..., x10.
According to the given information, the mean of these observations is 20. This means that the sum of these observations is 10 * 20 = 200.
We are also given that the standard deviation of these observations is 2. The standard deviation is calculated using the formula:
s.d. = sqrt((Σ(xi - mean)^2) / n)
where Σ represents the sum, xi represents each observation, mean represents the mean of the observations, and n represents the number of observations.
Using this formula, we can calculate the sum of the squared differences from the mean:
2^2 * 10 = (Σ(xi - 20)^2)
4 * 10 = Σ(xi^2 - 40xi + 400)
40 = Σ(xi^2 - 40xi + 400)
40 = Σxi^2 - 40Σxi + 400
Now, let's consider the new set of observations obtained by multiplying each observation by p and then reducing it by q. The new observations can be denoted by y1, y2, ..., y10.
yi = (xi * p) - q
The mean of the new observations can be calculated as follows:
mean of yi = (Σ((xi * p) - q)) / 10
mean of yi = (p * Σxi - 10q) / 10
Since the mean of the new observations is also given as 20, we can equate the above equation to 20:
(p * Σxi - 10q) / 10 = 20
p * Σxi - 10q = 200
p * Σxi = 200 + 10q
Σxi = (200 + 10q) / p
Now, let's consider the sum of the squared differences from the mean of the new observations:
Σ(yi - mean of yi)^2 = Σ(((xi * p) - q) - mean of yi)^2
Σ(yi - mean of yi)^2 = Σ(((xi * p) - q) - ((p * Σxi - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - (p * Σxi - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - (p * (200 + 10q) / p - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - (200 + 10q - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - 200 / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - 20))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - (q + 20)))^2
Σ(yi - mean of yi)^2 = Σ(xi^2 * p^2
According to the given information, the mean of these observations is 20. This means that the sum of these observations is 10 * 20 = 200.
We are also given that the standard deviation of these observations is 2. The standard deviation is calculated using the formula:
s.d. = sqrt((Σ(xi - mean)^2) / n)
where Σ represents the sum, xi represents each observation, mean represents the mean of the observations, and n represents the number of observations.
Using this formula, we can calculate the sum of the squared differences from the mean:
2^2 * 10 = (Σ(xi - 20)^2)
4 * 10 = Σ(xi^2 - 40xi + 400)
40 = Σ(xi^2 - 40xi + 400)
40 = Σxi^2 - 40Σxi + 400
Now, let's consider the new set of observations obtained by multiplying each observation by p and then reducing it by q. The new observations can be denoted by y1, y2, ..., y10.
yi = (xi * p) - q
The mean of the new observations can be calculated as follows:
mean of yi = (Σ((xi * p) - q)) / 10
mean of yi = (p * Σxi - 10q) / 10
Since the mean of the new observations is also given as 20, we can equate the above equation to 20:
(p * Σxi - 10q) / 10 = 20
p * Σxi - 10q = 200
p * Σxi = 200 + 10q
Σxi = (200 + 10q) / p
Now, let's consider the sum of the squared differences from the mean of the new observations:
Σ(yi - mean of yi)^2 = Σ(((xi * p) - q) - mean of yi)^2
Σ(yi - mean of yi)^2 = Σ(((xi * p) - q) - ((p * Σxi - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - (p * Σxi - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - (p * (200 + 10q) / p - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - (200 + 10q - 10q) / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - 200 / 10))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - q - 20))^2
Σ(yi - mean of yi)^2 = Σ((xi * p) - (q + 20)))^2
Σ(yi - mean of yi)^2 = Σ(xi^2 * p^2
Free Test
FREE
| Start Free Test |
Community Answer
The mean and the standard deviation (s.d.) of 10 observations are 20 a...
μ = 20, σ2 = 2
And pμ - q = 20/2 ⇒ 20p - q = 10
Also,
|p| σ2 = |p| × 2 = 1 ⇒
If p = 1/2 ⇒ q = 0 (rejected)
And pμ - q = 20/2 ⇒ 20p - q = 10
Also,
|p| σ2 = |p| × 2 = 1 ⇒
If p = 1/2 ⇒ q = 0 (rejected)
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer?
Question Description
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer?.
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer?.
Solutions for The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The mean and the standard deviation (s.d.) of 10 observations are 20 and 2, respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal toa)-10b)-20c)-5d)10Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup