The following table gives the percentage of on-time arrivals in U.S airports from 2004 through 2013.
Year 2004 2005 2006 2007 2008
On time arrivals/% 76.13 74.35 77.11 70.33 70.55
Year 2009 2010 2011 2012 2013
On time arrivals/% 79.69 76.75 75.46 84.93 80.33
Average - 765.63/10 = 76.563% but how do I set up the formula to find the standard deviation?
From Google:
To calculate the standard deviation of those numbers:
Work out the Mean (the simple average of the numbers)
Then for each number: subtract the Mean and square the result.
Then work out the mean of those squared differences.
Take the square root of that and we are done!
To calculate the standard deviation, you can follow these steps:
1. Calculate the mean (average) of the data set. In this case, the mean is 76.563%.
2. Subtract the mean from each individual data point and square the result.
For example:
- For 2004: (76.13 - 76.563)^2 = 0.183369
- For 2005: (74.35 - 76.563)^2 = 4.874369
- For 2006: (77.11 - 76.563)^2 = 0.301369
- For 2007: (70.33 - 76.563)^2 = 38.833369
- For 2008: (70.55 - 76.563)^2 = 36.043369
- For 2009: (79.69 - 76.563)^2 = 9.820369
- For 2010: (76.75 - 76.563)^2 = 0.034369
- For 2011: (75.46 - 76.563)^2 = 1.215769
- For 2012: (84.93 - 76.563)^2 = 69.330369
- For 2013: (80.33 - 76.563)^2 = 14.177369
3. Sum all the squared differences.
Sum = 0.183369 + 4.874369 + 0.301369 + 38.833369 + 36.043369 + 9.820369 + 0.034369 + 1.215769 + 69.330369 + 14.177369
4. Divide the sum by the number of data points (n).
n = 10 in this case.
5. Finally, take the square root of the result to find the standard deviation.
I hope this helps!
To find the standard deviation, you need to follow these steps:
Step 1: Calculate the mean (average) of the dataset. In this case, you have already calculated the average as 76.563%.
Step 2: Calculate the difference between each data point and the mean. For each data point, subtract the mean from that data point.
Step 3: Square each of the differences obtained in Step 2. This is done to eliminate negative values and emphasize deviations from the mean.
Step 4: Calculate the average of the squared differences obtained in Step 3. This is called the variance.
Step 5: Take the square root of the variance calculated in Step 4. This will give you the standard deviation.
Now, let's go through these steps using the given data:
Step 1: The mean is already calculated as 76.563%.
Step 2: Subtract the mean from each data point:
2004: 76.13 - 76.563 = -0.433
2005: 74.35 - 76.563 = -2.213
2006: 77.11 - 76.563 = 0.547
2007: 70.33 - 76.563 = -6.233
2008: 70.55 - 76.563 = -6.013
2009: 79.69 - 76.563 = 3.127
2010: 76.75 - 76.563 = 0.187
2011: 75.46 - 76.563 = -1.103
2012: 84.93 - 76.563 = 8.367
2013: 80.33 - 76.563 = 3.767
Step 3: Square each of the differences obtained in Step 2:
2004: (-0.433)^2 = 0.187
2005: (-2.213)^2 = 4.888
2006: (0.547)^2 = 0.299
2007: (-6.233)^2 = 38.800
2008: (-6.013)^2 = 36.156
2009: (3.127)^2 = 9.775
2010: (0.187)^2 = 0.035
2011: (-1.103)^2 = 1.217
2012: (8.367)^2 = 69.993
2013: (3.767)^2 = 14.180
Step 4: Calculate the average of the squared differences (variance):
Variance = (0.187 + 4.888 + 0.299 + 38.800 + 36.156 + 9.775 + 0.035 + 1.217 + 69.993 + 14.180) / 10 = 18.7536
Step 5: Take the square root of the variance to get the standard deviation:
Standard Deviation = √(18.7536) = 4.331%
So, the standard deviation of the given dataset is approximately 4.331%.