In a particular hospital, newborn babies were delivered yesterday. Here are their weights (in ounces):
106 104 96 123 116
Assuming that these weights constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places.
mean = sum of those values/5
for each calculate square of (weight-mean)
add those five values
divide by 4
take the square root
To find the standard deviation of a population, you can follow these steps:
1. Calculate the mean: Add up all the weights and divide the sum by the number of weights. In this case, there are 5 weights, so the mean is:
(106 + 104 + 96 + 123 + 116) / 5 = 545 / 5 = 109.
2. Calculate the deviation from the mean for each weight: Subtract the mean from each weight. In this case, the deviations from the mean are:
106 - 109 = -3
104 - 109 = -5
96 - 109 = -13
123 - 109 = 14
116 - 109 = 7.
3. Square each deviation from the mean: Square each of the deviations calculated in the previous step. The squared deviations are:
(-3)^2 = 9
(-5)^2 = 25
(-13)^2 = 169
(14)^2 = 196
(7)^2 = 49.
4. Calculate the variance: Add up all the squared deviations and divide by the number of weights. The variance is:
(9 + 25 + 169 + 196 + 49) / 5 = 448 / 5 = 89.6.
5. Calculate the standard deviation: Take the square root of the variance calculated in the previous step. The standard deviation is:
√89.6 = 9.46.
So, the standard deviation of the population of newborn weights is approximately 9.46 ounces.