no idea, but there are lots of handy calculators online.
Or, you can just do the work, and we can check your answer ...
The data list shows the scores of ten students in Mr. Smith's math class.
61, 67, 81, 83, 87, 88, 89, 90, 98, 100
What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students?
4 answers
Steve why would we let you check our answers if you cant even help figure it out?
yey
As an AI language model, I can provide step-by-step instructions on how to calculate the standard deviation of a sample:
1. Find the mean (average) of the data by adding up all the scores and dividing by the total number of scores:
mean = (61 + 67 + 81 + 83 + 87 + 88 + 89 + 90 + 98 + 100) / 10
mean = 83.4
2. Subtract the mean from each score to get the deviations from the mean:
deviations = (61-83.4), (67-83.4), (81-83.4), (83-83.4), (87-83.4), (88-83.4), (89-83.4), (90-83.4), (98-83.4), (100-83.4)
deviations = -22.4, -16.4, -2.4, -0.4, 3.6, 4.6, 5.6, 6.6, 14.6, 16.6
3. Square each deviation:
squared deviations = 22.4^2, 16.4^2, 2.4^2, 0.4^2, 3.6^2, 4.6^2, 5.6^2, 6.6^2, 14.6^2, 16.6^2
squared deviations = 501.76, 268.96, 5.76, 0.16, 12.96, 21.16, 31.36, 43.56, 213.16, 275.56
4. Add up all the squared deviations:
sum of squared deviations = 501.76 + 268.96 + 5.76 + 0.16 + 12.96 + 21.16 + 31.36 + 43.56 + 213.16 + 275.56
sum of squared deviations = 1369.36
5. Divide the sum of squared deviations by (n-1), where n is the number of scores in the sample:
variance = sum of squared deviations / (n-1)
variance = 1369.36 / 9
variance = 152.15
6. Take the square root of the variance to get the standard deviation:
standard deviation = square root of variance
standard deviation = square root of 152.15
standard deviation = 12.33 (rounded to the nearest tenth)
Therefore, the standard deviation of the sample is approximately 12.3.
1. Find the mean (average) of the data by adding up all the scores and dividing by the total number of scores:
mean = (61 + 67 + 81 + 83 + 87 + 88 + 89 + 90 + 98 + 100) / 10
mean = 83.4
2. Subtract the mean from each score to get the deviations from the mean:
deviations = (61-83.4), (67-83.4), (81-83.4), (83-83.4), (87-83.4), (88-83.4), (89-83.4), (90-83.4), (98-83.4), (100-83.4)
deviations = -22.4, -16.4, -2.4, -0.4, 3.6, 4.6, 5.6, 6.6, 14.6, 16.6
3. Square each deviation:
squared deviations = 22.4^2, 16.4^2, 2.4^2, 0.4^2, 3.6^2, 4.6^2, 5.6^2, 6.6^2, 14.6^2, 16.6^2
squared deviations = 501.76, 268.96, 5.76, 0.16, 12.96, 21.16, 31.36, 43.56, 213.16, 275.56
4. Add up all the squared deviations:
sum of squared deviations = 501.76 + 268.96 + 5.76 + 0.16 + 12.96 + 21.16 + 31.36 + 43.56 + 213.16 + 275.56
sum of squared deviations = 1369.36
5. Divide the sum of squared deviations by (n-1), where n is the number of scores in the sample:
variance = sum of squared deviations / (n-1)
variance = 1369.36 / 9
variance = 152.15
6. Take the square root of the variance to get the standard deviation:
standard deviation = square root of variance
standard deviation = square root of 152.15
standard deviation = 12.33 (rounded to the nearest tenth)
Therefore, the standard deviation of the sample is approximately 12.3.