Find the population standard deviation for the data set?
1, 2, 3, 5, 6, 7
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 population standard deviation for the given data set, you can follow these steps:
1. Calculate the mean (average) of the data set. Add up all the numbers in the data set and divide the sum by the total number of values. In this case, the sum is 1 + 2 + 3 + 5 + 6 + 7 = 24, and there are 6 values. So, the mean is 24/6 = 4.
2. Subtract the mean from each individual data point and square the result. This gives you the squared deviation for each value. For example, for the value 1, the squared deviation is (1 - 4)^2 = 9. Similarly, for the value 2, the squared deviation is (2 - 4)^2 = 4.
3. Calculate the sum of all the squared deviations. In this case, the sum is 9 + 4 + 1 + 1 + 4 + 9 = 28.
4. Divide the sum of squared deviations by the number of values (also known as the population size). In this case, the population size is 6. So, the variance is 28/6 = 4.67.
5. Finally, take the square root of the variance to get the population standard deviation. The population standard deviation for the given data set is approximately √4.67 ≈ 2.16.
So, the population standard deviation for the data set {1, 2, 3, 5, 6, 7} is approximately 2.16.