Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
22, 29, 21, 24, 27, 28, 25, 36
A. 4.8
B. 4.2
C. 2.8
D. 1.6
A. 4.8
4.44
To find the standard deviation for the given data, follow these steps:
Step 1: Find the mean (average) of the data.
Add up all the data points and divide by the total number of data points:
22 + 29 + 21 + 24 + 27 + 28 + 25 + 36 = 212
Mean = 212 / 8 = 26.5
Step 2: Find the difference between each data point and the mean.
Subtract the mean from each data point:
22 - 26.5 = -4.5
29 - 26.5 = 2.5
21 - 26.5 = -5.5
24 - 26.5 = -2.5
27 - 26.5 = 0.5
28 - 26.5 = 1.5
25 - 26.5 = -1.5
36 - 26.5 = 9.5
Step 3: Square each of the differences.
Square each of the differences calculated in Step 2:
(-4.5)^2 = 20.25
(2.5)^2 = 6.25
(-5.5)^2 = 30.25
(-2.5)^2 = 6.25
(0.5)^2 = 0.25
(1.5)^2 = 2.25
(-1.5)^2 = 2.25
(9.5)^2 = 90.25
Step 4: Find the average of the squared differences.
Add up all the squared differences and divide by the total number of data points:
(20.25 + 6.25 + 30.25 + 6.25 + 0.25 + 2.25 + 2.25 + 90.25) / 8 = 158.5 / 8 = 19.8125
Step 5: Take the square root of the average of the squared differences.
Square root of 19.8125 = 4.456281
Step 6: Round the answer to one more decimal place than the original data.
Rounding 4.456281 to one more decimal place gives 4.5.
Therefore, the standard deviation for the given data is 4.5.
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Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.