STAT141 Chapter Notes - Chapter 6: Standard Deviation, Unimodality
Document Summary
Standard deviation as a ruler and normal model. Shifting data: adding/subtracting a constant (c) to every data value adds/subtracts same constant to measures positions increase/decrease measures of mean, median, percentiles, max, and min. Rescaling data: multiply/divide all the data values by any constant (d), all measures of position and measures of spread are multiplied/divided by that constant everything (note: s2 = constant2) Rescale and shift: ynew = d x yoriginal + c. Standardizing (z-score): measures the direction and number of standard deviations away from the mean. Z-score = (observation mean) / standard deviation. Positive z-score: observation is above the mean. Negative z-score: observation is below the mean. Z-score of 0: observation is on the mean. Normal model/distribution: symmetric, unimodal, bell shaped notation: n (mean, standard deviation) The standardized value (z) follows a standard normal distribution (z~n(0,1)) Area for any normal distribution: use table d/table z after restating problem and standardizing values.
