Calculating Standard Deviation Homework

In summary, the conversation discusses calculating the standard deviation using a given formula and a set of data. The attempt at a solution includes two lists of numbers and the calculation of the total, uncorrected standard deviation, and corrected standard deviation. However, there are errors in the calculations and it is unclear what the data represents. The conversation also discusses the need to divide by n-1 for an unbiased estimator.
  • #1
EdmureTully
20
0

Homework Statement



I have to calculate the standard deviation

Homework Equations



http://0.tqn.com/d/statistics/1/0/M/-/-/-/standarddev.GIF

The Attempt at a Solution



0.64 0.4096
2.06 4.2436
0.16 0.0256
3.24 10.4976
1.74 3.0276
1.06 1.1236
4.04 16.3216
1.56 2.4336
1.3 1.69
3.64 13.2496
3.16 9.9856
3.04 9.2416
0.86 0.7396
3.56 12.6736
2.94 8.6436
1.74 3.0276
2.96 8.7616
2.34 5.4756
6.46 41.7316
2.76 7.6176

total = 151.9204

uncorrected sd = 2.75
corrected sd = 2.83

1 89.20
2 86.50 2.70
3 88.40 1.90
4 91.80 3.40
5 90.30 1.50
6 87.50 2.80
7 92.60 5.10
8 87.00 5.60
9 89.80 2.80
10 92.20 2.40
11 85.40 6.80
12 91.60 6.20
13 87.70 3.90
14 85.00 2.70
15 91.50 6.50
16 90.30 1.20
17 85.60 4.70
18 90.90 5.30
19 82.10 8.80
20 85.80 3.70

the answer they get is 2.91

average is 88.56

did i make any calculation error?

I can't believe i made any calculation error
 
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  • #2
Yes, you made some errors. Your value for the mean is correct. One of your differences is off, and you compounded that error by not summing the squares accurately.

It would have helped if you described what you were doing instead of just posting arrays of unlabeled numbers and leaving it to others to decipher what you did.
 
  • #3
Ok, thanks. One last thing, do I have to divide by n-1 or just n?
 
  • #4
For an unbiased estimator, you need to divide by n-1.
 
  • #5
EdmureTully said:

Homework Statement



I have to calculate the standard deviation

Homework Equations



http://0.tqn.com/d/statistics/1/0/M/-/-/-/standarddev.GIF

The Attempt at a Solution



0.64 0.4096
2.06 4.2436
0.16 0.0256
3.24 10.4976
1.74 3.0276
1.06 1.1236
4.04 16.3216
1.56 2.4336
1.3 1.69
3.64 13.2496
3.16 9.9856
3.04 9.2416
0.86 0.7396
3.56 12.6736
2.94 8.6436
1.74 3.0276
2.96 8.7616
2.34 5.4756
6.46 41.7316
2.76 7.6176

total = 151.9204

uncorrected sd = 2.75
corrected sd = 2.83

1 89.20
2 86.50 2.70
3 88.40 1.90
4 91.80 3.40
5 90.30 1.50
6 87.50 2.80
7 92.60 5.10
8 87.00 5.60
9 89.80 2.80
10 92.20 2.40
11 85.40 6.80
12 91.60 6.20
13 87.70 3.90
14 85.00 2.70
15 91.50 6.50
16 90.30 1.20
17 85.60 4.70
18 90.90 5.30
19 82.10 8.80
20 85.80 3.70

the answer they get is 2.91

average is 88.56

did i make any calculation error?

I can't believe i made any calculation error

What on Earth is your data? Is the first data set a list of 40 numbers (presented as two lists of 20, or is it two separate lists, each of size 20? If it is a single list of size 40 I get a total of 210.1804; if it is two lists of size 20 each I get a total of 49.26 for the first list and a total of 160.92094 for the second list. None of these match what you claim---but your analysis is totally meaningless because you do not give any clues as to what you are doing.
 

Related to Calculating Standard Deviation Homework

1. What is standard deviation?

Standard deviation is a measure of how spread out a set of data values are from the mean or average value. It is calculated by finding the difference between each data point and the mean, squaring those differences, finding the average of those squared differences, and then taking the square root of that average.

2. Why is standard deviation important?

Standard deviation is important because it helps us understand the variability or dispersion of a set of data. It can also help us compare different sets of data by giving us a common measure of spread. In addition, it is used in many statistical calculations and is a key component in many statistical models.

3. How do you calculate standard deviation?

To calculate standard deviation, you first need to find the mean or average of the data set. Then, for each data point, subtract the mean and square the difference. Find the average of those squared differences, and then take the square root of that average. This will give you the standard deviation for the data set.

4. What does a high or low standard deviation mean?

A high standard deviation means that the data points are spread out over a wider range, indicating a greater amount of variability or dispersion. A low standard deviation means that the data points are clustered closely around the mean, indicating less variability or dispersion.

5. How is standard deviation used in data analysis?

Standard deviation is used in data analysis to understand the spread and distribution of data, as well as to compare different data sets. It is often used in conjunction with other statistical measures, such as the mean and median, to gain a better understanding of the data and make more accurate conclusions and predictions.

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