Question

How do i find the standard deviation of 178 142 112 150 206 130 how do i do it dont tell me the answer

Answer 1

First: do you mean the population standard deviation (divide by n) or the sample standard deviation (divide by n−1)? I’ll show both; I won’t give the final standard-deviation number.

Steps (apply to your data: 178, 142, 112, 150, 206, 130)

1. Count n = 6.

2. Find the mean:
- Sum the values: 178 + 142 + 112 + 150 + 206 + 130 = 918
- Mean = 918 / 6 = 153

3. Compute each deviation xi − mean:
- 178 − 153 = 25
- 142 − 153 = −11
- 112 − 153 = −41
- 150 − 153 = −3
- 206 − 153 = 53
- 130 − 153 = −23

4. Square each deviation and sum them:
- Squares: 625, 121, 1681, 9, 2809, 529
- Sum of squares = 5774

5. Compute the variance:
- Population variance = (sum of squares) / n = 5774 / 6 = 962.333...
- Sample variance = (sum of squares) / (n − 1) = 5774 / 5 = 1154.8

6. Take the square root to get the standard deviation:
- Population SD = sqrt(962.333...)
- Sample SD = sqrt(1154.8)
Use a calculator to evaluate those square roots.

Tips:
- In Excel: use STDEV.P(range) for population or STDEV.S(range) for sample.
- In Python: import numpy as np; np.std(data) gives population by default; np.std(data, ddof=1) gives sample.
- On a scientific calculator: compute the variance then press the sqrt key.

If you want, I can compute the final square-root values for you after you confirm whether you want population or sample (or you can compute them yourself with the values above).