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Standard Deviation
To determine how much our measurements deviates from the mean value there is a measure which we need when we use statistical tests this measure is called the standard deviation.
Definition:
Standard deviation is a measure which describes how much individual measurements differ, on the average from the mean.
Suppose we contributed some money for a picnic in Abasyn University, in this contribution the following 11 students contributed their money in US Dollars
1. Fazal Rehman = 13
2. Mutahira Shaheen = 14
3. Anila = 14
4. Abu Zar = 15
5. Noroz = 16
6. Adnan = 16
7. Wahidi= 16
8. Farooque = 17
9. Shazia = 17
10. Hadia = 18
11. Mufti Zubair = 20
Now to determine the standard deviation we have to complete the following steps
A- we will first find the mean, which is the sum of all the individual measurements divided by the total number of measurements
Now let’s add all the measurements, 13+14+14+15+16+16+16+17+17+18+20 = 176
Now divide this sum by the total number by the total number of the contributors in our case the total contributors are 11 and the total dollar are 176 so the mean which is = to the total amount contributed divide by the number of contributors therefore the mean is 176/11 = 16
So the mean Dollars which our class contributed is
= 16 Dollars
B. we have calculated the mean which is 16, now doctor Nayyar wants to determine the standard deviation for which he has to calculate the individual distance of the amount from the mean, this can be determined by subtracting the individual value from the mean
hence go like this
1. Fazal Rehman = 13 -16 = -3
2. Mutahira Shaheen = 14-16 = -2
3. Anila = 14-16 = -2
4. Abu Zar = 15-16 = -1
5. Noroz = 16-16 = 0
6. Adnan = 16-16 = 0
7. Wahidi= 16- 16 = 0
8. Farooque = 17- 16 = +1
9. Shazia = 17-16 = +1
10. Hadia = 18 – 16 = +2
11. Mufti Zubair = 20 -16 = + 4
………………………………………………………………………..
Now ignore the plus or minus sign…………………………………..
Now for standard deviation square all the differences
1. Fazal Rehman = 13 -16 = 3x3 = 9
2.Mutahira Shaheen = 14-16 = 2x 2 = 4
3. Anila = 14-16 = 2 x 2 = 4
4. Abu Zar = 15-16 = 1x 1 = 1
5. Noroz = 16-16 = 0x 0 = 0
6. Adnan = 16-16 = 0 x 0 =0
7. Wahidi= 16- 16 = 0x 0 = 0
8. Farooque = 17- 16 = 1x 1 = 1
9. Shazia = 17-16 = 1 x 1 = 1
10. Hadia = 18 – 16 = 2 x 2 = 4
11. Mufti Zubair = 20 -16 = 4 x 4 = 16
The next step is to add all the squared values
So come up do it quickly
9 + 4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 4 + 16 = 40
After adding all the differences we have to divide this sum by the total number of contributors minus – 1
As we have 11 contributors and 11 – 1 = 10
So we go like this
Sum of all the squared values divided by total number of values minus one , we get 40/ 10 = 4
Finally we take the square root to obtain the Standard deviation
√ 4 = 2 dollars
Now Dr Nayyar understood that how much the individual contributors on average deviated from the mean amount contributed, which is 2 dollars
A large standard deviation means that there is a wide scatter of measured values around the mean, while a small standard deviation means that the individual value is concentrated around the mean.
For example if the amount of dollars contributed was
10, 11, 12, 14, 16, 16, 16, 18, 20, 21
The mean dollar would still have been 16 dollars but the standard deviation would have been 4 dollars, indicating a much larger variation in the observation.
We are united hence we had a very small standard deviation, except Mufti Zubair. Ha Ha Ha,
Now go for Picnic and enjoy statistics and before doing that convert your currency in Pakistani Rupees to avoid problems in shopping.
Good Night.
To determine how much our measurements deviates from the mean value there is a measure which we need when we use statistical tests this measure is called the standard deviation.
Definition:
Standard deviation is a measure which describes how much individual measurements differ, on the average from the mean.
Suppose we contributed some money for a picnic in Abasyn University, in this contribution the following 11 students contributed their money in US Dollars
1. Fazal Rehman = 13
2. Mutahira Shaheen = 14
3. Anila = 14
4. Abu Zar = 15
5. Noroz = 16
6. Adnan = 16
7. Wahidi= 16
8. Farooque = 17
9. Shazia = 17
10. Hadia = 18
11. Mufti Zubair = 20
Now to determine the standard deviation we have to complete the following steps
A- we will first find the mean, which is the sum of all the individual measurements divided by the total number of measurements
Now let’s add all the measurements, 13+14+14+15+16+16+16+17+17+18+20 = 176
Now divide this sum by the total number by the total number of the contributors in our case the total contributors are 11 and the total dollar are 176 so the mean which is = to the total amount contributed divide by the number of contributors therefore the mean is 176/11 = 16
So the mean Dollars which our class contributed is
= 16 Dollars
B. we have calculated the mean which is 16, now doctor Nayyar wants to determine the standard deviation for which he has to calculate the individual distance of the amount from the mean, this can be determined by subtracting the individual value from the mean
hence go like this
1. Fazal Rehman = 13 -16 = -3
2. Mutahira Shaheen = 14-16 = -2
3. Anila = 14-16 = -2
4. Abu Zar = 15-16 = -1
5. Noroz = 16-16 = 0
6. Adnan = 16-16 = 0
7. Wahidi= 16- 16 = 0
8. Farooque = 17- 16 = +1
9. Shazia = 17-16 = +1
10. Hadia = 18 – 16 = +2
11. Mufti Zubair = 20 -16 = + 4
………………………………………………………………………..
Now ignore the plus or minus sign…………………………………..
Now for standard deviation square all the differences
1. Fazal Rehman = 13 -16 = 3x3 = 9
2.Mutahira Shaheen = 14-16 = 2x 2 = 4
3. Anila = 14-16 = 2 x 2 = 4
4. Abu Zar = 15-16 = 1x 1 = 1
5. Noroz = 16-16 = 0x 0 = 0
6. Adnan = 16-16 = 0 x 0 =0
7. Wahidi= 16- 16 = 0x 0 = 0
8. Farooque = 17- 16 = 1x 1 = 1
9. Shazia = 17-16 = 1 x 1 = 1
10. Hadia = 18 – 16 = 2 x 2 = 4
11. Mufti Zubair = 20 -16 = 4 x 4 = 16
The next step is to add all the squared values
So come up do it quickly
9 + 4 + 4 + 1 + 0 + 0 + 0 + 1 + 1 + 4 + 16 = 40
After adding all the differences we have to divide this sum by the total number of contributors minus – 1
As we have 11 contributors and 11 – 1 = 10
So we go like this
Sum of all the squared values divided by total number of values minus one , we get 40/ 10 = 4
Finally we take the square root to obtain the Standard deviation
√ 4 = 2 dollars
Now Dr Nayyar understood that how much the individual contributors on average deviated from the mean amount contributed, which is 2 dollars
A large standard deviation means that there is a wide scatter of measured values around the mean, while a small standard deviation means that the individual value is concentrated around the mean.
For example if the amount of dollars contributed was
10, 11, 12, 14, 16, 16, 16, 18, 20, 21
The mean dollar would still have been 16 dollars but the standard deviation would have been 4 dollars, indicating a much larger variation in the observation.
We are united hence we had a very small standard deviation, except Mufti Zubair. Ha Ha Ha,
Now go for Picnic and enjoy statistics and before doing that convert your currency in Pakistani Rupees to avoid problems in shopping.
Good Night.
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