Suppose that S = (VI. '0' 2. '0'3) is a linearly independent set of vectors in a vector space V. Is T = (WI. W2. w)l. where WI = VI + '0'2. W, = '0'1+ '0'). W) = v,+vJ.linearly dependent or linearly independent? Justify your answer.
Ch. 3 ➔ Appropriate measures depend on the shape ◆ Symmetric: mean and standard deviation ◆ Skewed: median and interquartile range ➔ The mean: The average ◆ Literally the balancing point ◆ For a symmetric distribution, the mean is at the center and close to typical values ◆ Also balances skewed graphs ● Doesn’t tell us the typical value ● Right skewed, the average is to the right of the typical values and vice versa ➔ Standard Deviation: number that measures how far away a typical observation is from the mean ◆ Typical distance ◆ Larger variance = larger standard deviation ◆ Larger standard deviation: more values farther from the mean ➔ Empirical rule and zscores ◆ Empirical rule: if a distribution is unimodal and symmetric then 68% fall into 1 standard deviation, 95% fall into 2 standard deviations, and 99.7% (or almost all) fall into 3 standard deviations ● Anything outside of two standard deviations is unusual ◆ Zscore is the number of standard deviations a data value is from the mean ● Standard units
