Answer :
The sample variance for the given set of weights is approximately 6.5734 pounds squared.
To calculate the sample variance, you can follow these steps:
Step 1: Find the mean of the sample weights.
Add up the weights of the seven infants and divide by the number of infants (which is 7 in this case):
9.1 + 12.1 + 13.1 + 14.1 + 10.1 + 15.1 + 16.1 = 89.7
Mean = 89.7 / 7 = 12.8143 (rounded to four decimal places)
Step 2: Calculate the deviation of each weight from the mean.
Subtract the mean (12.8143) from each weight to get the deviation:
9.1 - 12.8143 = -3.7143
12.1 - 12.8143 = -0.7143
13.1 - 12.8143 = 0.2857
14.1 - 12.8143 = 1.2857
10.1 - 12.8143 = -2.7143
15.1 - 12.8143 = 2.2857
16.1 - 12.8143 = 3.2857
Step 3: Square each deviation.
Square each of the deviations calculated in Step 2:
(-3.7143)^2 = 13.7953
(-0.7143)^2 = 0.5102
(0.2857)^2 = 0.0816
(1.2857)^2 = 1.6541
(-2.7143)^2 = 7.3716
(2.2857)^2 = 5.2245
(3.2857)^2 = 10.8031
Step 4: Sum up the squared deviations.
Add up all the squared deviations:
13.7953 + 0.5102 + 0.0816 + 1.6541 + 7.3716 + 5.2245 + 10.8031 = 39.4404
Step 5: Calculate the sample variance.
Divide the sum of squared deviations by (n-1), where n is the number of observations (in this case, 7):
Sample Variance = 39.4404 / (7-1) = 6.5734 (rounded to four decimal places)
Therefore, the sample variance for the given set of weights is approximately 6.5734 pounds squared.
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