The participants in a weight-loss class lost the following weights (in pounds) after three weeks of dieting:
1,5,2,1,3,6
Assuming that these weights constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places. How do I break down this to find my answer
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.
To find the standard deviation of a population, you would need to follow these steps:
Step 1: Find the mean of the data set.
Step 2: Subtract the mean from each data point.
Step 3: Square each of the differences obtained in Step 2.
Step 4: Find the mean of the squared differences obtained in Step 3.
Step 5: Take the square root of the mean obtained in Step 4.
Let's break down the steps to find the standard deviation of the given weight-loss class data set:
Step 1: Find the mean of the data set.
Add up all the weights: 1 + 5 + 2 + 1 + 3 + 6 = 18.
Divide the sum by the number of data points (6 in this case): 18 / 6 = 3.
So, the mean (average) weight loss is 3 pounds.
Step 2: Subtract the mean from each data point.
Subtract the mean from each weight:
1 - 3 = -2
5 - 3 = 2
2 - 3 = -1
1 - 3 = -2
3 - 3 = 0
6 - 3 = 3
Step 3: Square each of the differences obtained in Step 2.
Square each of the differences:
(-2)^2 = 4
2^2 = 4
(-1)^2 = 1
(-2)^2 = 4
0^2 = 0
3^2 = 9
Step 4: Find the mean of the squared differences obtained in Step 3.
Add up the squared differences: 4 + 4 + 1 + 4 + 0 + 9 = 22.
Divide the sum by the number of data points: 22 / 6 = 3.67 (rounded to two decimal places).
Step 5: Take the square root of the mean obtained in Step 4.
Calculate the square root: √3.67 ≈ 1.92 (rounded to two decimal places).
Therefore, the standard deviation of the weight-loss class population is approximately 1.92 pounds.