Can someone help me with this questions.
Find the variance for a given data. Rpund your answer to one more decimal place then the original data.
Compute the variance. Jeanne is currently taking college zoology. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following score.
17 10 7 14 3
Variance = [ƒ°(X-ƒÊ)^2]/N
This involves finding the mean, subtracting each score from the mean, squaring each of those scores, adding them up and dividing that sum by the number of scores.
To get the standard deviation (SD), find the square root of the variance.
I hope this helps. Thanks for asking.
To compute the variance for the given data:
Step 1: Find the mean.
To find the mean, sum up all the numbers and divide by the total number of scores.
Mean = (17 + 10 + 7 + 14 + 3) / 5
= 51 / 5
= 10.2
Step 2: Subtract the mean from each score, then square the differences.
(17 - 10.2)^2 = 48.04
(10 - 10.2)^2 = 0.04
(7 - 10.2)^2 = 10.24
(14 - 10.2)^2 = 14.44
(3 - 10.2)^2 = 52.09
Step 3: Find the sum of the squared differences.
Sum of (X - mean)^2 = 48.04 + 0.04 + 10.24 + 14.44 + 52.09
= 124.85
Step 4: Divide the sum of squared differences by the total number of scores minus 1.
Variance = Sum of (X - mean)^2 / (Total number of scores - 1)
= 124.85 / (5 - 1)
= 124.85 / 4
= 31.21
Step 5: Round the variance to one more decimal place than the original data.
Rounded variance = 31.2 (to one decimal place)
Therefore, the variance for the given data is 31.2 (rounded).
To find the variance for the given data, you can follow these steps:
Step 1: Find the mean
- Add up all the scores: 17 + 10 + 7 + 14 + 3 = 51
- Divide the sum by the number of scores (in this case, 5): 51 ÷ 5 = 10.2
- The mean score is 10.2
Step 2: Calculate the differences from the mean
- Subtract the mean from each score:
- For 17: 17 - 10.2 = 6.8
- For 10: 10 - 10.2 = -0.2
- For 7: 7 - 10.2 = -3.2
- For 14: 14 - 10.2 = 3.8
- For 3: 3 - 10.2 = -7.2
Step 3: Square the differences
- Square each difference:
- For 6.8: (6.8)^2 = 46.24
- For -0.2: (-0.2)^2 = 0.04
- For -3.2: (-3.2)^2 = 10.24
- For 3.8: (3.8)^2 = 14.44
- For -7.2: (-7.2)^2 = 51.84
Step 4: Calculate the sum of the squared differences
- Add up all the squared differences:
- 46.24 + 0.04 + 10.24 + 14.44 + 51.84 = 122.8
Step 5: Divide the sum by the number of scores minus 1
- Divide the sum of squared differences by the number of scores minus 1 (in this case, 5 - 1 = 4):
- 122.8 ÷ 4 = 30.7
So, the variance for the given data is 30.7 (rounded to one more decimal place than the original data).