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?
no idea, but there are lots of handy calculators online.
Or, you can just do the work, and we can check your answer ...
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.
To calculate the standard deviation of a sample, you can follow these steps:
1. Find the mean of the scores by adding up all the numbers and dividing the sum by the total number of scores. In this case, the sum is 61 + 67 + 81 + 83 + 87 + 88 + 89 + 90 + 98 + 100 = 844. Since there are 10 scores, the mean is 844/10 = 84.4.
2. Subtract the mean from each score to get the differences. For example, the first score, 61, has a difference of 61 - 84.4 = -23.4.
3. Square each difference. For example, (-23.4)^2 = 547.56.
4. Find the sum of all the squared differences. In this case, the sum is 547.56 + 2.56 + 0.36 + 1.96 + 2.56 + 3.24 + 4.84 + 29.16 + 148.84 + 205.16 = 946.4.
5. Divide the sum of squared differences by (n-1), where n is the number of scores in the sample. Since there are 10 scores, the division is 946.4 / (10-1) = 105.16.
6. Finally, take the square root of the result you obtained in the previous step to find the standard deviation. In this case, the square root of 105.16 is approximately 10.3.
Therefore, the standard deviation of the data, to the nearest tenth, is 10.3.