How do you find these?

Question

1. Sample mean, xbar= ∑(x) / n
2. sample variance, s²=∑(x-xbar)² / n-1
3. sample std dev, s=√s²
4. ^{margin of error}

^{could you give examples??}

Answer 1

For a Sample S, equal to {1 3 6 9 10 12 15 17 18 20} with Sample Size of n = 10:

Sample Mean x_bar is given by [∑x]/n equal to [1+3+6+9+10+12+15+17+18+20]÷10 or 111/10 or 11.1.

Sample Variance is given by [∑(x−x_bar)²]÷(n−1) or [(1−11.1)²+(3−11.1)²+(6−11.1)²+(9−11.1)²+(10−11.1)²+(12−11.1)²+(15−11.1)²+(17−11.1)²+(18−11.1)²+(20−11.1)²]÷(10−1), equal to 41.877777777777... (For Sample Variance, divide by (n-1); for Population Variance, divide by n.)

Sample Standard Deviation s_x-bar is given by the Square Root Of The Sample Variance or √41.87777777777 equal to 6.471304179.

Margin Of Error Of A Confidence Interval is given by ±zs_x-bar where z is the number of Standard Deviation Units from the Sample Mean. For a 95% Confidence Interval, the Margin Of Error is equal to ±1.96√41.87777777777 or ±12.68375619.