What is the standard deviation of the data set: 1, 2, 3, 4, 5?
Practice Questions
1 question
Q1
What is the standard deviation of the data set: 1, 2, 3, 4, 5?
1
1.5
2
2.5
Mean = 3. Standard Deviation = sqrt[((1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2)/5] = sqrt[2] = 1.414.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the standard deviation of the data set: 1, 2, 3, 4, 5?
Solution: Mean = 3. Standard Deviation = sqrt[((1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2)/5] = sqrt[2] = 1.414.
Steps: 6
Step 1: Find the mean (average) of the data set. Add all the numbers together: 1 + 2 + 3 + 4 + 5 = 15. Then divide by the number of values (5): 15 / 5 = 3. So, the mean is 3.
Step 2: Subtract the mean from each number in the data set to find the difference: (1-3), (2-3), (3-3), (4-3), (5-3) which gives us: -2, -1, 0, 1, 2.
Step 3: Square each of the differences: (-2)^2 = 4, (-1)^2 = 1, (0)^2 = 0, (1)^2 = 1, (2)^2 = 4. So, we have: 4, 1, 0, 1, 4.
Step 4: Add all the squared differences together: 4 + 1 + 0 + 1 + 4 = 10.
Step 5: Divide the total by the number of values (5): 10 / 5 = 2. This is the variance.
Step 6: Take the square root of the variance to find the standard deviation: sqrt(2) = approximately 1.414.
