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GDB Spring 2014 Dated: Aug 07, 14

Topic for Graded Discussion Board

 

Since variance and standard deviation both are used to check variability in the data set. Discuss which one is more reliable to apply. Justify your answer at least with two appropriate examples."

 

Opening Date of Graded Discussion Board:  Monday, August 11, 2014 at 12:01 a.m.

Closing Date of Graded Discussion Board:    Tuesday, August 12, 2014 at 11:59 p.m.



 

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Replies to This Discussion

Calculating Standard Deviation

The standard deviation is calculated simply by taking the square root of the value that you get when you calculate the variance. Programs like Microsoft Excel and SPSS calculate both the variance and the standard deviation for you, and are very useful when working with large data sets as they tend to be more accurate than calculating the standard deviation by hand.

Conceptual Difference Between Standard Deviation and Variance

The variance of a data set measures the mathematical dispersion of the data relative to the mean. However, though this value is theoretically correct, it is difficult to apply in a real-world sense because the values used to calculate it were squared. The standard deviation, as the square root of the variance gives a value that is in the same units as the original values, which makes it much easier to work with and easier to interpret in conjunction with the concept of the normal curve

In the special case of data that are approximately normally distributed, we can use the 68- 95-99.7 rule to say more about the approximate % of values in the data set that are within 1, 2, and 3 standard deviations of the mean.

formula .SD
x = individual scores
M = mean
n = number of scores in group

Steps

Create two columns: x & (x-M)2
  1. Put the raw data in the x column
  2. Calculate the mean
  3. Calculate deviation scores by subtracting each score from the mean and squaring it and put these in the second column
  4. Sum the squared deviation scores
  5. Set up the formula
  6. Calculate s

Example

scores: 4,5,5,4,4,2,2,6

x
(x-M)2
4
0
5
1
5
1
4
0
4
0
2
4
2
4
6
4
M = 4
S(x-M)2 = 14
SD = 1.32

standard deviation 1.32

They can be factors used to determine if there is a statistically important difference between mean values (the standard deviation is used in the computation of a confidence interval) such as Student's t test. Or if variances can be assumed or not assumed to be equal in doing Student's t test: you can evaluate this assumption by using the F test, where you compare variances of samples. So the values come in handy.

The main advantage of the standard deviation is that it is in the same units as the thing you are measuring.. For example, if you are measuring a length in cm, the standard deviation would be expressed in cm but the variance would be in (cm)^2

Standard Deviation
The standard deviation of your data is the square root of the variance, and therefore it reflects both the deviation from the mean and the frequency of this deviation. Standard deviation is often used instead of the variance because the scale of the variance tends to be larger than the scale of the raw data, while the standard deviation is on the same scale as most of the data. The formula for standard deviation is:

standard deviation = sq root (variance)

For example, with the data set (1,1,1, 5), the standard deviation is the square root of 3 = 1.73

Thanks for your reply tariq bhai..... you are always of great help to students but no one has uploaded the complete assignment????

unho ne gdb me examples pochi hai plz koi examples btaye ga 

 For Sample

 Data:    6, 7, 5, 3, 4

 

  s^2 = Ʃ (xi - x) ^2/n-1

 

 Mean = 6+7+5+3+4 = 25/5 = 5

 

Variance= =(6-5)^2+=(7-5)^2+=(5-5)^2+=(3-5)^2+=(4-5)^2/5 -1 = 2.5

                               

 S.D= √2.5 = 1.58

 

 For Population

 Data:    6, 7, 5, 3, 4

 Mean = 6+7+5+3+4 = 25/5 = 5

                           

  Ợ^2 = Ʃ (ni - µ) ^2/N

 

  =(6-5)^2+=(7-5)^2+=(5-5)^2+=(3-5)^2+=(4-5)^2/5 = 2

                       

Variance= 2

 

 S.D= √2 = 1.41

Standard Deviation is just the square root of Variance and also Standard deviation is more reliable then variance. The both are used to check variability in the data set.  Therefore both are reflects deviation from the mean and the frequency of this deviation. The main feature of the S.D is that you can measure units as the fixation you are required...  If you are measuring a length in cm, the standard deviation would be expressed in cm but the variance would be in (cm) ^2 so, the S.D is more reliable as compared to variance.

 MTH302-GDB No.1 Spring 2014 Due Date of Graded Discussion Board is Tuesday, August 12

Conceptual Difference Between Standard Deviation and Variance
The variance of a data set measures the mathematical dispersion of the data relative to the mean. However, though this value is theoretically correct, it is difficult to apply in a real-world sense because the values used to calculate it were squared. The standard deviation, as the square root of the variance gives a value that is in the same units as the original values, which makes it much easier to work with and easier to interpret in conjunction with the concept of the normal curve.



They can be factors used to determine if there is a statistically important difference between mean values (the standard deviation is used in the computation of a confidence interval) such as Student's t test. Or if variances can be assumed or not assumed to be equal in doing Student's t test: you can evaluate this assumption by using the F test, where you compare variances of samples. So the values come in handy.


Difference Between Standard Deviation and Variance
The variance of a data set measures the mathematical dispersion of the data relative to the mean. However, though this value is theoretically correct, it is difficult to apply in a real-world sense because the values used to calculate it were squared. The standard deviation, as the square root of the variance gives a value that is in the same units as the original values, which makes it much easier to work with and easier to interpret in conjunction with the concept of the normal curve.
Standard deviation
is a measurement used in statistics of the amount a number varies from the average number in a series of numbers . the standard deviation tells those interpreting the data how reliable the data is or how much difference there is between the pieces of data by showing how close to the average all of the data is
there is a two example :-
1 : A low standard deviation means that the data is very closely related to the average, thus very reliable.
2 : A high standard deviation means that there is a large variance between the data and the statistical average,thus not as reliable.



The main advantage of the standard deviation is that it is in the same units as the thing you are measuring.. For example, if you are measuring a length in cm, the standard deviation would be expressed in cm but the variance would be in (cm)^2

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