Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
07 Sep 2022, 16:56
Kudos
Bookmarks
I saw a problem somewhere along the lines where if you have a set of numbers and each number is increased by a factor of 9 that the standard deviation will increase, but the problem noted that you must assume the set has different numbers.
With this said, if the set did not have different numbers (disregarding having all zeroes in a set), what would happen?
If you multiplied everything by a factor of 1/2 or -2, what would happen to these sets if you 1.) had all different numbers in the sets and 2.) if the numbers were all the same (besides having a set with all zeroes).
Thank you for your time and help.
Any other major takeaways that I should be aware of with standard deviation problems?
With this said, if the set did not have different numbers (disregarding having all zeroes in a set), what would happen?
If you multiplied everything by a factor of 1/2 or -2, what would happen to these sets if you 1.) had all different numbers in the sets and 2.) if the numbers were all the same (besides having a set with all zeroes).
Thank you for your time and help.
Any other major takeaways that I should be aware of with standard deviation problems?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
07 Sep 2022, 21:27
Kudos
Bookmarks
woohoo921
Standard Deviation is a measure which shows how much variation from the mean exists. The standard deviation indicates a typical deviation from the mean.
Steps to calculate Standard Deviation:
1) Calculate the mean of numbers in the set.
2) Subtract mean from each number. the result is the deviation of each number from the mean.
3) Square all the deviations and find the average of all the deviations. The average of all deviations is called the variance.
4) Standard deviation= Square root of the Variance.
Adding or subtracting same number to all the number in the set
Case 1 - If all the numbers in the set are equal.
Let Set A= (4,4,4), the mean of the numbers in Set A is 4 and Deviations of each number from the mean is 0, the variance will be zero and hence the Standard deviation will be zero.
If we add let say a number 2 to all the number in the set, then the numbers become (6,6,6), the mean of the numbers become 6 and Deviations of each number from the mean is still 0, the variance will be zero and hence the Standard deviation will be zero.
Similarly if we subtract a number say -2, the standard deviation will be the same.
So there is no change in the Standard deviation.
Case 2 - If all the numbers in the set are different.
Let Set A= (1,2,3), the mean of the numbers in Set A is 2 and Deviations of each number 1,2,3 from the mean is -1,0,1 respectively, the variance will be 2/3 and hence the Standard deviation will be \(\sqrt{2/3}\).
If we add let say a number 2 to all the number in the set, then the numbers become (3,4,5), the mean of the numbers becomes 4 and Deviations of number 3, 4, 5 from the mean becomes -1,0,1 , the variance will be 2/3 and hence the Standard deviation will still remain \(\sqrt{2/3}\).
So there is no change in the Standard deviation.
Similarly if we subtract a number say -1, the standard deviation will be the same.
Conclusion: When adding or subtracting a number to a set of number the standard deviation won't change.
Multiplying same number to all the number in the set
Case 1 - If all the numbers in the set are equal.
Let Set A= (4,4,4), the mean of the numbers in Set A is 4 and Deviations of each number from the mean is 0, the variance will be zero and hence the Standard deviation will be zero.
If we multiply let say a number 2 to all the number in the set, then the numbers become (8,8,8), the mean of the numbers become 8 and Deviations of each number from the mean is still 0, the variance will be zero and hence the Standard deviation will be zero.
Similarly if we multiply a number say 1/2, the standard deviation will be the same.
So there is no change in the Standard deviation.
Case 2 - If all the numbers in the set are different.
Let Set A= (1,2,3), the mean of the numbers in Set A is 2 and Deviations of each number 1,2,3 from the mean is -1,0,1 respectively, the variance will be 2/3 and hence the Standard deviation will be \(\sqrt{2/3}\).
If we multiply let say a number 2 to all the number in the set, then the numbers become (2,4,6), the mean of the numbers becomes 4 and Deviations of number 2, 4, 6 from the mean becomes -2,0,2 , the variance will be 8/3 and hence the Standard deviation will be \(\sqrt{8/3}\) i.e \(2*\sqrt{2/3}\)
So the Standard deviation is now 2 times the earlier standard deviation.
Similarly if we multiply a number say 1/2, the standard deviation will become \(1/2*\sqrt{2/3}\).
Conclusion: When multiplying a set of numbers by any number, the standard deviation will also change by same factor only if the numbers in the set are all not same. If all the numbers are same then there will not be any change in standard deviation.
I hope this is helpful.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
