Home




How to calculate standard deviation

Standard Deviation of a probability distribution measures the distribution of data from the mean value. Probability distribution maps the probability of a variable within a particular range of values.

For Example: Suppose we toss a coin two times

All possible outcomes: HH, HT, TH, TT
Total number of outcomes = 4
Let a variable, X measures the number of heads in this experiment
Probability of n heads = (Outcomess with n heads)/ (Total number of outcomes)

Number of Heads                  Probability
 (X)                                
(Probability of n heads)             
 
    0                                  0.25                                                
    1                                  0.5
    2                                  0.25

For a probability distribution, plot number of Heads(X) on the x-axis and the probability of n heads on the y-axis.

Range of values in this case = 0-2

Consider a data set with following value

2, 2, 4, 5, 3, 6, 13

Step 1: Count the number of elements in the data set
N = 7

Step 2: Find the mean or average of the data set

Arithmetic Mean (average) = (2 + 2 + 4 + 5 + 3 + 6 + 13)/7  
                                         = 35/7 = 5

Step 3: Subtract Mean from each element in the data set and square the result

(2 – 5) = -3   :   (-3) ^ 2 = 9
(2 – 5) = -3   :   (-3) ^ 2 = 9
(4 – 5) = -1   :   (-1) ^ 2 = 1
(5 – 5) = 0    :   (0) ^ 2 = 0
(3 – 5) = -2   :   (-2) ^ 2 = 4
(6 – 5) = 1    :    (1) ^ 2 = 1
(13 –5) = 8   :    (8) ^ 2 = 64


For Sample Set

Step 4: Divide the sum of the resulting values with one less than the number of elements in the data set and find the square root

SD(Standard Deviation) = Sqrt ((9 + 9 + 1 + 0 + 4 + 1 + 64)/6)
      = 3.82

Variance is the square of standard deviation = SD ^ 2 = 14.59

For Complete Set

Step 4: Divide the sum of the resulting values with the number of elements in the data set and find the square root

SD(Population Standard Deviation) = Sqrt ((9 + 9 + 1 + 0 + 4 + 1 + 64)/7)
      = 3.54

Population variance is the square of standard deviation = SD ^ 2
                                                                             = 12.25

Example of Sample Set: Sample voters in an exit poll
Example of Complete Set: Set of all the voters in an election

Essential GMAT Reading Comprehension Guide


After reading F1GMAT’s Essential GMAT Reading Comprehension Guide, you will:

1. Complete GMAT RC Questions in less than 1 minute and 50 seconds
2. Read Faster
3. Take Notes Effectively
4. Collect and Interpret Facts
5. Speed up Summary Creation
6. Remember Information
7. Question the Author   
8. Learn to Answer GMAT Reading Comprehension Title question   
9. Learn to Answer GMAT Reading Comprehension Main Idea Question   

10.Learn to Answer GMAT Reading comprehension Inference question

11. Learn to Answer GMAT Reading Comprehension Detail Question   

12. Learn to Answer GMAT Reading Comprehension Purpose Question
12. Learn to Answer GMAT organization of passage Question
13. Learn to identify the style/tone or attitude of the author

Download Essential GMAT Reading Comprehension Guide (2019 Edition) (100+ New Questions)









Mastering GMAT Critical Reasoning



After you read F1GMAT’s Mastering GMAT Critical Reasoning Guide, you will learn:

How to overcome flawed thinking in GMAT Critical Reasoning?  


How to spot Inconsistencies in Arguments  

How to eliminate out of scope answer choices using Necessary and Sufficient Conditions  

How to Paraphrase GMAT Critical Reasoning Question  

How to Answer Assumption Question Type  

How to Answer Conclusion Question Type  

How to Answer Inference Question Type  

How to Answer Strengthen Question Type  

How to Answer Weaken Question Type  

How to Answer bold-faced and Summary Question Types  

How to Answer Parallel Reasoning Questions  

How to Answer the Fill in the Blanks Question


Download Mastering GMAT Critical Reasoning (2019 Edition) (25+ New Questions)




Navigate F1GMAT


F1GMAT Services (MBA Applicants) 


F1GMAT's Books

MBA Salary(Latest Salary Data)
 
MBA Admission Interview Tips

Funding 

Deadlines

MBA Application Essays


MBA Recommendation Letter

GMAT Tutorials

GMAT Question Bank

Top MBA Programs

Get F1GMAT's Newsletters (Best in the Industry)
Included in the Newsletter:

  • Ranking Analysis
  • Post-MBA Salary Trends
  • Post-MBA Job Function & Industry Analysis
  • Post-MBA City Review
  • MBA Application Essay Tips
  • School Specific Essay Tips
  • GMAT Preparation Tips
  • MBA Admission Interview Tips
  • School Specific Interview Tips
  • Funding Guidance and
  • Special Consultation Service (only for Subscribers)

Subscribe to F1GMAT's Newsletter