第7章描述性统计 Descriptive Statistics
第7章 描述性统计 Descriptive Statistics
、集中趋势( Central Tendency) 1 What is the most typical value? The Average: A typical value for quantitative data The Weighted Average: Adjusting for importance The Median: A typical value for quantitative and ordinal data The Mode: A typical value even for nominal data 2 What percentile is it? Extremes, Quartiles, and Box Plots e The Cumulative distribution function displays the percentiles
一、集中趋势(Central Tendency ) 1、What is the most typical value? ◆ The Average: A typical value for quantitative data ◆ The Weighted Average: Adjusting for importance ◆ The Median: A typical value for quantitative and ordinal data ◆ The Mode: A typical value even for nominal data 2、What percentile is it? ◆ Extremes, Quartiles, and Box Plots ◆ The Cumulative distribution function displays the percentiles
平均值或均数( Average or Mean) Add the data, divide by n or N(the number of elementary units X1+X2+..+X X (样本) Sample average X1+X2+…+XN (总体) Population average Divides total equally. The only such summary .A representative, central number (if data set is approximately norma l近似正态分布) ◆ Summation notation 1x=1x ∑ is capital Greek sign
平均值或均数（Average or Mean） ◆ Add the data, divide by n or N (the number of elementary units) ◆ Divides total equally. The only such summary ◆ A representative, central number (if data set is approximately normal近似正态分布) ◆ Summation notation ⚫ S is capital Greek sigma n X X X X + + + n = ... 1 2 N X + X + + X N = ... 1 2 （样本） Sample average （总体）Population average = = n i Xi n X 1 1 = = N i Xi N 1 1
Example:次品数( Number of Defects) Defects measured for each of 10 production lots 4.1.3.7.3.0.7.14.5.9 10 20 Defects per lot Average is 5.1 defects per lot
Example: 次品数（Number of Defects） ◆ Defects measured for each of 10 production lots 4, 1, 3, 7, 3, 0, 7, 14, 5, 9 0 2 0 5 10 15 20 Defects per lot Frequency (lots) Average is 5.1 defects per lot
中位数( Median) e Also summarizes the data ◆ The middle one:强它是一个位置指标! Pu d ut data in order (先排序) ● Pick middle one( or average middle two if n is even(偶数)) Median(9, 4, 5)=Median(4, 5,9)=5 5+7 Median(9,4,5,7)= Median(4,5,7,9)=276 ◆Rank(秩) of the median is(1+m)2 o If n=3, rank is(1+3)/2=2 o If n=4, rank is(1+4)/2-2.5(so average 2nd and 3rd) Ifn=262, rank is(1+262)2=131.5
中位数（Median） ◆ Also summarizes the data ◆ The middle one：强调它是一个位置指标！ ⚫ Put data in order（先排序） ⚫ Pick middle one (or average middle two if n is even（偶数)） ⚫ Median (9, 4, 5) = Median(4, 5, 9) = 5 ⚫ Median (9, 4, 5, 7) = Median (4, 5, 7, 9) = = 6 ◆ Rank（秩） of the median is (1+n)/2 ⚫ If n=3, rank is (1+3)/2 = 2 ⚫ If n=4, rank is (1+4)/2 = 2.5 (so average 2nd and 3rd) ⚫ If n=262, rank is (1+262)/2 = 131.5 5+7 2