正态分布( Normal Distribution) Average, median, and mode are identica o If the data come from a normal distribution Average. median and mode are identical in the case of a normal distribution
正态分布（Normal Distribution） ◆ Average, median, and mode are identical ⚫ If the data come from a normal distribution Average, median, and mode are identical in the case of a normal distribution
偏态分布( Skewed Distribution) Average, median, and mode are different The few large(or small) values influence the mean more than the median e The highest point is not in the center Average Median Mode
偏态分布（Skewed Distribution） ◆ Average, median, and mode are different ⚫ The few large (or small) values influence the mean more than the median ⚫ The highest point is not in the center Average Median Mode
有哪些集中趋势指标? ◆ Average o Best for normal data ● Preserves totals(保留所有样品信息) ◆ Median o Good for skewed data or data with outliers, provided you do not need to preserve or estimate total amounts ◆Mode e Best for categories(nominal data) o The mode is the only summary computable for nominal data
有哪些集中趋势指标？ ◆ Average ⚫ Best for normal data ⚫ Preserves totals（保留所有样品信息） ◆ Median ⚫ Good for skewed data or data with outliers, provided you do not need to preserve or estimate total amounts ◆ Mode ⚫ Best for categories (nominal data). ⚫ The mode is the only summary computable for nominal data!
Which Summary? (continued Average requires quantitative data(numbers) e Median works with quantitative or ordinal e Mode works with quantitative. ordinal. or nominal Quantitative Ordinal Nominal Average Ye es Median Yes Yes Mode Ye es Yes Yes
Which Summary? (continued) ◆ Average requires quantitative data (numbers) ◆ Median works with quantitative or ordinal ◆ Mode works with quantitative, ordinal, or nominal Quantitative Ordinal Nominal Average Yes - - Median Yes Yes - Mode Yes Yes Yes
加权平均( Weighted Average) o Ordinary average gives same weight to all elementary units X=-X1+-X2+…+Xn o Weighted average allows different weights X=W,X, +w,X++wX Weights must add up to 1 1+2+y If not then divide each b ir total(规一化)
加权平均（Weighted Average） ◆ Ordinary average gives same weight to all elementary units ◆ Weighted average allows different weights ◆ Weights must add up to 1 ⚫ If not, then divide each by their total（规一化） Xn n X n X n X 1 ... 1 1 1 2 = + + + X w X w X wnXn = + + ... + 1 1 2 2 ... 1 1 2 + + + = w w wn