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billionaire999
Joined: 26 Mar 2021
Last visit: 12 May 2021
Posts: 39
Given Kudos: 24
Location: India
Schools: Rotman '24 Desautels Melbourne HEC Montreal Ivey '24 Rotman
17 Apr 2021, 23:19
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Hello everyone.
I find the topic of standard deviation very difficult and its formulas impossible to memorise.
Can someone help me with what is essential to know in the topic and what all can be left alone in my journey to score 750.
I find the topic of standard deviation very difficult and its formulas impossible to memorise.
Can someone help me with what is essential to know in the topic and what all can be left alone in my journey to score 750.
19 Apr 2021, 04:26
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Here are 3 concepts / steps that you will find useful when solving Standard Deviation Questions
Concept 1. How to compute Standard Deviation?
Step 1: Compute mean for the given set of numbers.
Step 2: Compute Deviation of each term from the mean. Deviation is computed by subtracting mean from each term. You will have as many deviations as the number of terms in the set.
Step 3: Square the deviations
Step 4: Compute the average of the squared deviations. This is the penultimate step. The result of this step is called Variance.
Step 5: Square root of Variance is the standard deviation.
Concept 2: If a constant 'k' is added or subtracted from each term in a set, the standard deviation does not change. Because, the relative difference between the numbers (and in turn the deviation from the mean) remain unchanged.
For example, let the original set comprise 3 numbers: 3, 4, 5. The mean is 4 and the deviations are -1, 0, and 1
Add 10 to each of the 3 terms, the revised numbers will be 13, 14, and 15. The mean is 15. But the deviations remain -1, 0, and 1
Concept 3: If a constant 'k' is multiplied to each term in a set, the standard deviation will become k times the initial SD. The relative difference between the numbers becomes k times the initial one.
For example, let the original set comprise 3 numbers: 3, 4, 5. The mean is 4 and the deviations are -1, 0, and 1
Multiply each element by 2. The revised numbers will be 6, 8, and 10. The new mean is 8. The deviations become -2, 0, and 2. So, the SD will change and the new SD will twice the old one.
A few questions may require you to compute SD. However, many questions will test whether you have understood what SD stands for (a measure of the extent of dispersion of data in a set) and will test application of concepts 2 and 3.
Cheers
Concept 1. How to compute Standard Deviation?
Step 1: Compute mean for the given set of numbers.
Step 2: Compute Deviation of each term from the mean. Deviation is computed by subtracting mean from each term. You will have as many deviations as the number of terms in the set.
Step 3: Square the deviations
Step 4: Compute the average of the squared deviations. This is the penultimate step. The result of this step is called Variance.
Step 5: Square root of Variance is the standard deviation.
Concept 2: If a constant 'k' is added or subtracted from each term in a set, the standard deviation does not change. Because, the relative difference between the numbers (and in turn the deviation from the mean) remain unchanged.
For example, let the original set comprise 3 numbers: 3, 4, 5. The mean is 4 and the deviations are -1, 0, and 1
Add 10 to each of the 3 terms, the revised numbers will be 13, 14, and 15. The mean is 15. But the deviations remain -1, 0, and 1
Concept 3: If a constant 'k' is multiplied to each term in a set, the standard deviation will become k times the initial SD. The relative difference between the numbers becomes k times the initial one.
For example, let the original set comprise 3 numbers: 3, 4, 5. The mean is 4 and the deviations are -1, 0, and 1
Multiply each element by 2. The revised numbers will be 6, 8, and 10. The new mean is 8. The deviations become -2, 0, and 2. So, the SD will change and the new SD will twice the old one.
A few questions may require you to compute SD. However, many questions will test whether you have understood what SD stands for (a measure of the extent of dispersion of data in a set) and will test application of concepts 2 and 3.
Cheers
General Discussion
18 Apr 2021, 02:11
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billionaire999
Generally for the GMAT you only need to understand the concept of SD: you won't be asked to actually calculate the standard deviation of a set on the GMAT. So, GMAT SD questions are much more conceptual than computational. What is the main thing you should know about it? Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
20. Descriptive Statistics
- Theory
Statistics Made Easy - All in One Topic!
GMAT Statistics 101
Math: Standard Deviation
How to Quickly Solve Standard Deviation Questions on the GMAT
For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
Hope it helps.
