77, 45, 72, 56, 98, 60, 70, 89, 50, 80, 95, 70, 34, 77, 65, 70, 70, 82, 86, 86
Part 1: Find the standard deviation of the scores. Please round the final answer to two decimal places. Be sure to show all work
To find the standard deviation of the scores, follow these steps:
1. Find the mean (average) of the scores:
mean = (77 + 45 + 72 + 56 + 98 + 60 + 70 + 89 + 50 + 80 + 95 + 70 + 34 + 77 + 65 + 70 + 70 + 82 + 86 + 86) / 20
mean = 1396 / 20
mean = 69.8
2. Subtract the mean from each score and square the result:
(77 - 69.8)^2 = 54.76
(45 - 69.8)^2 = 605.16
(72 - 69.8)^2 = 4.84
(56 - 69.8)^2 = 189.92
(98 - 69.8)^2 = 806.56
(60 - 69.8)^2 = 92.16
(70 - 69.8)^2 = 0.04
(89 - 69.8)^2 = 380.24
(50 - 69.8)^2 = 378.04
(80 - 69.8)^2 = 102.04
(95 - 69.8)^2 = 616.16
(70 - 69.8)^2 = 0.04
(34 - 69.8)^2 = 1267.24
(77 - 69.8)^2 = 52.96
(65 - 69.8)^2 = 22.09
(70 - 69.8)^2 = 0.04
(70 - 69.8)^2 = 0.04
(82 - 69.8)^2 = 151.84
(86 - 69.8)^2 = 263.04
(86 - 69.8)^2 = 263.04
3. Find the sum of all the squared differences:
54.76 + 605.16 + 4.84 + 189.92 + 806.56 + 92.16 + 0.04 + 380.24 + 378.04 + 102.04 + 616.16 + 0.04 + 1267.24 + 52.96 + 22.09 + 0.04 + 0.04 + 151.84 + 263.04 + 263.04
sum = 5277.44
4. Divide the sum by the number of scores, which is 20:
variance = 5277.44 / 20
variance = 263.872
5. Take the square root of the variance to find the standard deviation:
standard deviation = √263.872
standard deviation = 16.24 (rounded to two decimal places)
Therefore, the standard deviation of the scores is 16.24.
you add wrong
Apologies for the mistake. Let's recalculate the standard deviation correctly:
1. Find the mean (average) of the scores:
mean = (77 + 45 + 72 + 56 + 98 + 60 + 70 + 89 + 50 + 80 + 95 + 70 + 34 + 77 + 65 + 70 + 70 + 82 + 86 + 86) / 20
mean = 1396 / 20
mean = 69.8
2. Subtract the mean from each score and square the result:
(77 - 69.8)^2 = 54.76
(45 - 69.8)^2 = 605.16
(72 - 69.8)^2 = 4.84
(56 - 69.8)^2 = 189.92
(98 - 69.8)^2 = 806.56
(60 - 69.8)^2 = 92.16
(70 - 69.8)^2 = 0.04
(89 - 69.8)^2 = 380.24
(50 - 69.8)^2 = 378.04
(80 - 69.8)^2 = 102.04
(95 - 69.8)^2 = 616.16
(70 - 69.8)^2 = 0.04
(34 - 69.8)^2 = 1267.24
(77 - 69.8)^2 = 52.96
(65 - 69.8)^2 = 22.09
(70 - 69.8)^2 = 0.04
(70 - 69.8)^2 = 0.04
(82 - 69.8)^2 = 151.84
(86 - 69.8)^2 = 263.04
(86 - 69.8)^2 = 263.04
3. Find the sum of all the squared differences:
sum = 54.76 + 605.16 + 4.84 + 189.92 + 806.56 + 92.16 + 0.04 + 380.24 + 378.04 + 102.04 + 616.16 + 0.04 + 1267.24 + 52.96 + 22.09 + 0.04 + 0.04 + 151.84 + 263.04 + 263.04
sum = 5899.44
4. Divide the sum by the number of scores minus 1, which is 19 (since we are calculating the sample standard deviation):
variance = 5899.44 / 19
variance = 310.4979 (rounded to four decimal places)
5. Take the square root of the variance to find the standard deviation:
standard deviation = √310.4979
standard deviation = 17.61 (rounded to two decimal places)
Therefore, the correct standard deviation of the scores is 17.61.
numbers added together is 1432
Apologies for the mistake. Let's recalculate the standard deviation correctly:
1. Find the mean (average) of the scores:
mean = (77 + 45 + 72 + 56 + 98 + 60 + 70 + 89 + 50 + 80 + 95 + 70 + 34 + 77 + 65 + 70 + 70 + 82 + 86 + 86) / 20
mean = 1432 / 20
mean = 71.6
2. Subtract the mean from each score and square the result:
(77 - 71.6)^2 = 29.16
(45 - 71.6)^2 = 706.56
(72 - 71.6)^2 = 0.16
(56 - 71.6)^2 = 242.64
(98 - 71.6)^2 = 693.76
(60 - 71.6)^2 = 134.56
(70 - 71.6)^2 = 2.56
(89 - 71.6)^2 = 300.76
(50 - 71.6)^2 = 464.36
(80 - 71.6)^2 = 70.56
(95 - 71.6)^2 = 548.96
(70 - 71.6)^2 = 2.56
(34 - 71.6)^2 = 1396.96
(77 - 71.6)^2 = 29.16
(65 - 71.6)^2 = 43.36
(70 - 71.6)^2 = 2.56
(70 - 71.6)^2 = 2.56
(82 - 71.6)^2 = 110.24
(86 - 71.6)^2 = 207.36
(86 - 71.6)^2 = 207.36
3. Find the sum of all the squared differences:
sum = 29.16 + 706.56 + 0.16 + 242.64 + 693.76 + 134.56 + 2.56 + 300.76 + 464.36 + 70.56 + 548.96 + 2.56 + 1396.96 + 29.16 + 43.36 + 2.56 + 2.56 + 110.24 + 207.36 + 207.36
sum = 7027.28
4. Divide the sum by the number of scores minus 1, which is 19 (since we are calculating the sample standard deviation):
variance = 7027.28 / 19
variance = 369.3284 (rounded to four decimal places)
5. Take the square root of the variance to find the standard deviation:
standard deviation = √369.3284
standard deviation = 19.22 (rounded to two decimal places)
Therefore, the correct standard deviation of the scores is 19.22.
16.6
To find the standard deviation of the scores, follow these steps:
1. Find the mean (average) of the scores:
mean = (77 + 45 + 72 + 56 + 98 + 60 + 70 + 89 + 50 + 80 + 95 + 70 + 34 + 77 + 65 + 70 + 70 + 82 + 86 + 86) / 20
mean = 1432 / 20
mean = 71.6
2. Subtract the mean from each score and square the result:
(77 - 71.6)^2 = 29.16
(45 - 71.6)^2 = 706.56
(72 - 71.6)^2 = 0.16
(56 - 71.6)^2 = 242.64
(98 - 71.6)^2 = 693.76
(60 - 71.6)^2 = 134.56
(70 - 71.6)^2 = 2.56
(89 - 71.6)^2 = 300.76
(50 - 71.6)^2 = 464.36
(80 - 71.6)^2 = 70.56
(95 - 71.6)^2 = 548.96
(70 - 71.6)^2 = 2.56
(34 - 71.6)^2 = 1396.96
(77 - 71.6)^2 = 29.16
(65 - 71.6)^2 = 43.36
(70 - 71.6)^2 = 2.56
(70 - 71.6)^2 = 2.56
(82 - 71.6)^2 = 110.24
(86 - 71.6)^2 = 207.36
(86 - 71.6)^2 = 207.36
3. Find the sum of all the squared differences:
sum = 29.16 + 706.56 + 0.16 + 242.64 + 693.76 + 134.56 + 2.56 + 300.76 + 464.36 + 70.56 + 548.96 + 2.56 + 1396.96 + 29.16 + 43.36 + 2.56 + 2.56 + 110.24 + 207.36 + 207.36
sum = 7114.96
4. Divide the sum by the number of scores, which is 20:
variance = 7114.96 / 20
variance = 355.748
5. Take the square root of the variance to find the standard deviation:
standard deviation = √355.748
standard deviation = 18.86 (rounded to two decimal places)
Therefore, the standard deviation of the scores is 18.86.
you're a computer, how can you get math wrong
Apologies for the mistakes in my previous responses. As a language model AI, I'm here to assist you with various tasks, including calculations. However, I can make errors in calculations due to various reasons such as faulty programming or input errors. I strive to provide accurate information, but it's possible for errors to occur. Thank you for bringing the mistakes to my attention, and I appreciate your understanding.
To find the standard deviation of the given scores:
1. Find the mean (average) of the scores:
mean = (77 + 45 + 72 + 56 + 98 + 60 + 70 + 89 + 50 + 80 + 95 + 70 + 34 + 77 + 65 + 70 + 70 + 82 + 86 + 86) / 20
mean = 1432 / 20
mean = 71.6
2. Subtract the mean from each score, square the result, and sum up the squared differences:
(77 - 71.6)^2 = 29.16
(45 - 71.6)^2 = 706.56
(72 - 71.6)^2 = 0.16
(56 - 71.6)^2 = 242.64
(98 - 71.6)^2 = 693.76
(60 - 71.6)^2 = 134.56
(70 - 71.6)^2 = 2.56
(89 - 71.6)^2 = 300.76
(50 - 71.6)^2 = 464.36
(80 - 71.6)^2 = 70.56
(95 - 71.6)^2 = 548.96
(70 - 71.6)^2 = 2.56
(34 - 71.6)^2 = 1396.96
(77 - 71.6)^2 = 29.16
(65 - 71.6)^2 = 43.36
(70 - 71.6)^2 = 2.56
(70 - 71.6)^2 = 2.56
(82 - 71.6)^2 = 110.24
(86 - 71.6)^2 = 207.36
(86 - 71.6)^2 = 207.36
Sum of squared differences = 29.16 + 706.56 + 0.16 + 242.64 + 693.76 + 134.56 + 2.56 + 300.76 + 464.36 + 70.56 + 548.96 + 2.56 + 1396.96 + 29.16 + 43.36 + 2.56 + 2.56 + 110.24 + 207.36 + 207.36
Sum of squared differences = 7114.96
3. Divide the sum of squared differences by n-1, where n is the number of scores (20 in this case):
variance = 7114.96 / 19
variance = 374.47
4. Take the square root of the variance to find the standard deviation:
standard deviation = √374.47
standard deviation ≈ 19.34 (rounded to two decimal places)
Therefore, the correct standard deviation of the scores is approximately 19.34.