Asked by AOL
Compute the range and sample standard deviation for strength of the concrete (in psi).
3990,4120, 3300, 3100, 2970, 3850, 4120, 4040
3990,4120, 3300, 3100, 2970, 3850, 4120, 4040
Answers
Answered by
AOL
your answer for standard deviation is wrong.
Answered by
AOL
your mean is wrong which cause your standard deviation to wrong.
Answered by
AOL
I got the mean =3686.25
Answered by
AOL
I believe yjour calculator is mess up. Your programmer really need to reprogram your calculator so that you stop make mistake in your calculation.
Answered by
GPT 3.5
To compute the range, we need to find the difference between the maximum and minimum values in the data set.
The maximum value is 4120 and the minimum value is 2970.
Range = Maximum value - Minimum value = 4120 - 2970 = 1150 psi
To compute the sample standard deviation, we need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data value and square the result.
3. Find the average of the squared differences.
4. Take the square root to find the standard deviation.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 35080 / 8
Mean = 4385 psi
Calculating the squared differences:
(3990 - 4385)^2 = (-395)^2 = 156025
(4120 - 4385)^2 = (-265)^2 = 70225
(3300 - 4385)^2 = (-1085)^2 = 1177225
(3100 - 4385)^2 = (-1285)^2 = 1651225
(2970 - 4385)^2 = (-1415)^2 = 2004225
(3850 - 4385)^2 = (-535)^2 = 286225
(4120 - 4385)^2 = (-265)^2 = 70225
(4040 - 4385)^2 = (-345)^2 = 119025
Calculating the average of the squared differences:
Sum of squared differences = 156025 + 70225 + 1177225 + 1651225 + 2004225 + 286225 + 70225 + 119025 = 5324425
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 5324425 / (8 - 1) = 760632.14
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 760632.14 ≈ 872.16 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is 872.16 psi.
The maximum value is 4120 and the minimum value is 2970.
Range = Maximum value - Minimum value = 4120 - 2970 = 1150 psi
To compute the sample standard deviation, we need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data value and square the result.
3. Find the average of the squared differences.
4. Take the square root to find the standard deviation.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 35080 / 8
Mean = 4385 psi
Calculating the squared differences:
(3990 - 4385)^2 = (-395)^2 = 156025
(4120 - 4385)^2 = (-265)^2 = 70225
(3300 - 4385)^2 = (-1085)^2 = 1177225
(3100 - 4385)^2 = (-1285)^2 = 1651225
(2970 - 4385)^2 = (-1415)^2 = 2004225
(3850 - 4385)^2 = (-535)^2 = 286225
(4120 - 4385)^2 = (-265)^2 = 70225
(4040 - 4385)^2 = (-345)^2 = 119025
Calculating the average of the squared differences:
Sum of squared differences = 156025 + 70225 + 1177225 + 1651225 + 2004225 + 286225 + 70225 + 119025 = 5324425
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 5324425 / (8 - 1) = 760632.14
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 760632.14 ≈ 872.16 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is 872.16 psi.
Answered by
GPT 3.5
I apologize for the mistake. Let's recalculate the sample standard deviation correctly.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 35090 / 8
Mean ≈ 4386.25 psi
Calculating the squared differences:
(3990 - 4386.25)^2 ≈ (-396.25)^2 ≈ 157007.56
(4120 - 4386.25)^2 ≈ (-266.25)^2 ≈ 70992.56
(3300 - 4386.25)^2 ≈ (-1086.25)^2 ≈ 1180458.56
(3100 - 4386.25)^2 ≈ (-1286.25)^2 ≈ 1654207.56
(2970 - 4386.25)^2 ≈ (-1416.25)^2 ≈ 2007846.56
(3850 - 4386.25)^2 ≈ (-536.25)^2 ≈ 287106.56
(4120 - 4386.25)^2 ≈ (-266.25)^2 ≈ 70992.56
(4040 - 4386.25)^2 ≈ (-346.25)^2 ≈ 119586.56
Calculating the average of the squared differences:
Sum of squared differences ≈ 157007.56 + 70992.56 + 1180458.56 + 1654207.56 + 2007846.56 + 287106.56 + 70992.56 + 119586.56 ≈ 6102208.52
Average of squared differences ≈ Sum of squared differences / (Number of data points - 1) ≈ 6102208.52 / (8 - 1) ≈ 871744.07
Calculating the standard deviation:
Sample standard deviation ≈ square root of the average of squared differences ≈ square root of 871744.07 ≈ 933.68 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is 933.68 psi.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 35090 / 8
Mean ≈ 4386.25 psi
Calculating the squared differences:
(3990 - 4386.25)^2 ≈ (-396.25)^2 ≈ 157007.56
(4120 - 4386.25)^2 ≈ (-266.25)^2 ≈ 70992.56
(3300 - 4386.25)^2 ≈ (-1086.25)^2 ≈ 1180458.56
(3100 - 4386.25)^2 ≈ (-1286.25)^2 ≈ 1654207.56
(2970 - 4386.25)^2 ≈ (-1416.25)^2 ≈ 2007846.56
(3850 - 4386.25)^2 ≈ (-536.25)^2 ≈ 287106.56
(4120 - 4386.25)^2 ≈ (-266.25)^2 ≈ 70992.56
(4040 - 4386.25)^2 ≈ (-346.25)^2 ≈ 119586.56
Calculating the average of the squared differences:
Sum of squared differences ≈ 157007.56 + 70992.56 + 1180458.56 + 1654207.56 + 2007846.56 + 287106.56 + 70992.56 + 119586.56 ≈ 6102208.52
Average of squared differences ≈ Sum of squared differences / (Number of data points - 1) ≈ 6102208.52 / (8 - 1) ≈ 871744.07
Calculating the standard deviation:
Sample standard deviation ≈ square root of the average of squared differences ≈ square root of 871744.07 ≈ 933.68 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is 933.68 psi.
Answered by
GPT 3.5
I apologize for the mistake. Let's recalculate the mean and then recompute the sample standard deviation correctly.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 31690 / 8
Mean = 3962.5 psi
Calculating the squared differences:
(3990 - 3962.5)^2 = (27.5)^2 = 756.25
(4120 - 3962.5)^2 = (157.5)^2 = 24806.25
(3300 - 3962.5)^2 = (-662.5)^2 = 438906.25
(3100 - 3962.5)^2 = (-862.5)^2 = 744806.25
(2970 - 3962.5)^2 = (-992.5)^2 = 985006.25
(3850 - 3962.5)^2 = (-112.5)^2 = 12656.25
(4120 - 3962.5)^2 = (157.5)^2 = 24806.25
(4040 - 3962.5)^2 = (77.5)^2 = 6015.625
Calculating the average of the squared differences:
Sum of squared differences = 756.25 + 24806.25 + 438906.25 + 744806.25 + 985006.25 + 12656.25 + 24806.25 + 6015.625 = 2274157.5
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 2274157.5 / (8 - 1) = 324879.64
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 324879.64 ≈ 570.17 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is approximately 570.17 psi.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 31690 / 8
Mean = 3962.5 psi
Calculating the squared differences:
(3990 - 3962.5)^2 = (27.5)^2 = 756.25
(4120 - 3962.5)^2 = (157.5)^2 = 24806.25
(3300 - 3962.5)^2 = (-662.5)^2 = 438906.25
(3100 - 3962.5)^2 = (-862.5)^2 = 744806.25
(2970 - 3962.5)^2 = (-992.5)^2 = 985006.25
(3850 - 3962.5)^2 = (-112.5)^2 = 12656.25
(4120 - 3962.5)^2 = (157.5)^2 = 24806.25
(4040 - 3962.5)^2 = (77.5)^2 = 6015.625
Calculating the average of the squared differences:
Sum of squared differences = 756.25 + 24806.25 + 438906.25 + 744806.25 + 985006.25 + 12656.25 + 24806.25 + 6015.625 = 2274157.5
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 2274157.5 / (8 - 1) = 324879.64
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 324879.64 ≈ 570.17 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is approximately 570.17 psi.
Answered by
GPT 3.5
Apologies for the incorrect calculation. Let's recalculate the mean and then recompute the sample standard deviation correctly.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 31190 / 8
Mean = 3898.75 psi
Calculating the squared differences:
(3990 - 3898.75)^2 = (91.25)^2 = 8330.62
(4120 - 3898.75)^2 = (221.25)^2 = 48933.12
(3300 - 3898.75)^2 = (-598.75)^2 = 358502.81
(3100 - 3898.75)^2 = (-798.75)^2 = 637506.56
(2970 - 3898.75)^2 = (-928.75)^2 = 862981.56
(3850 - 3898.75)^2 = (-48.75)^2 = 2376.56
(4120 - 3898.75)^2 = (221.25)^2 = 48933.12
(4040 - 3898.75)^2 = (141.25)^2 = 19977.81
Calculating the average of the squared differences:
Sum of squared differences = 8330.62 + 48933.12 + 358502.81 + 637506.56 + 862981.56 + 2376.56 + 48933.12 + 19977.81 = 2645461.16
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 2645461.16 / (8 - 1) = 378080.16
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 378080.16 ≈ 614.80 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is approximately 614.80 psi.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 31190 / 8
Mean = 3898.75 psi
Calculating the squared differences:
(3990 - 3898.75)^2 = (91.25)^2 = 8330.62
(4120 - 3898.75)^2 = (221.25)^2 = 48933.12
(3300 - 3898.75)^2 = (-598.75)^2 = 358502.81
(3100 - 3898.75)^2 = (-798.75)^2 = 637506.56
(2970 - 3898.75)^2 = (-928.75)^2 = 862981.56
(3850 - 3898.75)^2 = (-48.75)^2 = 2376.56
(4120 - 3898.75)^2 = (221.25)^2 = 48933.12
(4040 - 3898.75)^2 = (141.25)^2 = 19977.81
Calculating the average of the squared differences:
Sum of squared differences = 8330.62 + 48933.12 + 358502.81 + 637506.56 + 862981.56 + 2376.56 + 48933.12 + 19977.81 = 2645461.16
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 2645461.16 / (8 - 1) = 378080.16
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 378080.16 ≈ 614.80 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is approximately 614.80 psi.
Answered by
GPT 3.5
I apologize for the repeated mistakes in my previous responses. I will recalculate the mean and the sample standard deviation correctly to ensure accuracy.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 31590 / 8
Mean = 3948.75 psi
Calculating the squared differences:
(3990 - 3948.75)^2 = (41.25)^2 = 1701.56
(4120 - 3948.75)^2 = (171.25)^2 = 29306.56
(3300 - 3948.75)^2 = (-648.75)^2 = 420663.56
(3100 - 3948.75)^2 = (-848.75)^2 = 720066.56
(2970 - 3948.75)^2 = (-978.75)^2 = 958011.56
(3850 - 3948.75)^2 = (-98.75)^2 = 9751.56
(4120 - 3948.75)^2 = (171.25)^2 = 29306.56
(4040 - 3948.75)^2 = (91.25)^2 = 8340.62
Calculating the average of the squared differences:
Sum of squared differences = 1701.56 + 29306.56 + 420663.56 + 720066.56 + 958011.56 + 9751.56 + 29306.56 + 8340.62 = 2452160.50
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 2452160.50 / (8 - 1) = 350308.64
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 350308.64 ≈ 591.75 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is approximately 591.75 psi.
Calculating the mean:
Mean = (3990 + 4120 + 3300 + 3100 + 2970 + 3850 + 4120 + 4040) / 8
Mean = 31590 / 8
Mean = 3948.75 psi
Calculating the squared differences:
(3990 - 3948.75)^2 = (41.25)^2 = 1701.56
(4120 - 3948.75)^2 = (171.25)^2 = 29306.56
(3300 - 3948.75)^2 = (-648.75)^2 = 420663.56
(3100 - 3948.75)^2 = (-848.75)^2 = 720066.56
(2970 - 3948.75)^2 = (-978.75)^2 = 958011.56
(3850 - 3948.75)^2 = (-98.75)^2 = 9751.56
(4120 - 3948.75)^2 = (171.25)^2 = 29306.56
(4040 - 3948.75)^2 = (91.25)^2 = 8340.62
Calculating the average of the squared differences:
Sum of squared differences = 1701.56 + 29306.56 + 420663.56 + 720066.56 + 958011.56 + 9751.56 + 29306.56 + 8340.62 = 2452160.50
Average of squared differences = Sum of squared differences / (Number of data points - 1) = 2452160.50 / (8 - 1) = 350308.64
Calculating the standard deviation:
Sample standard deviation = square root of the average of squared differences ≈ square root of 350308.64 ≈ 591.75 psi
Therefore, the range of the concrete strength is 1150 psi and the sample standard deviation is approximately 591.75 psi.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.