《医学统计学》 三、样本均数的分布

从同一总体里随机抽取n相同的许多样本，这些样本均数吴正态分布。如前面所述正常人红细胞数的抽样实验中已求得100个样本均数，其中多数与总体均数μ比较接近而集中分布在其周围，且左右基本对称，见表6.3（此表由表6.4中的100个均数划记归组而得）。

表6.3　红细胞抽样实验中100个样本均数的分布

组　段460-470-480-490-500-510-520-530-540-合计样本数1318282813711100

表6.4　一百个样本的均数、标准差、95%可信区间

样本号均数标准差95%可信区间样本号均数标准差95%可信区间1488.661.65444.49～532.712498.333.97474.01～522.593509.450.96472.96～545.844498.452.63460.76～536.045494.929.51473.80～516.006°546.743.23515.78～577.62*7524.533.60500.45～548.55*8488.341.04458.94～517.669485.355.14445.85～524.7510502.648.55467.88～537.3211495.140.63466.03～524.1712524.737.81497.65～551.7513512.753.18474.65～550.7514494.837.24468.15～521.4515493.639.94465.03～522.1716495.329.47474.22～516.3817491.019.32477.18～504.8218506.553.83468.00～545.0019487.539.39461.32～517.6820495.932.70472.51～519.2921504.834.76479.94～529.6622512.244.76483.17～547.2323496.540.65467.41～525.5924499.837.04473.31～526.2925505.737.21479.08～532.3226487.734.50463.02～512.3827501.537.35474.79～528.2128476.129.64454.91～497.29*29523.251.57486.31～560.0930509.533.61485.45～533.5531494.228.60473.75～514.6532506.225.29483.10～524.3033501.127.88481.15～521.0534520.630.23498.98～542.2235492.042.18461.82～522.1836509.619.17495.89～523.3137488.642.29458.36～518.8438510.947.55476.88～544.9239516.439.96487.81～544.9940518.846.43485.59～552.0141495.936.89469.53～522.2742°526.442.78495.80～557.0043505.853.84467.30～544.3044503.047.33469.14～536.8645504.847.77470.62～538.9846492.429.20471.52～513.2847505.538.32478.08～532.9248486.552.98448.59～524.4149515.238.69487.51～542.8950487.053.75448.55～525.4551503.351.54466.43～540.1752491.058.47449.18～532.8253522.365.01475.79～568.8154490.349.92454.58～526.0255516.737.26490.05～543.3556489.631.41467.14～512.0657490.062.90445.01～534.9958489.230.91467.09～511.3159509.140.51480.12～538.0860513.529.18492.62～534.3861476.442.06446.32～506.4862511.528.46491.14～531.8663480.744.83448.62～512.7864501.429.00480.66～522.1465481.150.65444.86～517.3466496.036.53469.87～522.1367489.244.20457.58～520.8268494.829.73473.54～516.0669497.268.49448.21～546.1970504.135.13478.95～529.2571507.934.35483.33～532.4772°465.325.56447.02～483.58*73502.645.54470.03～535.1774486.448.51451.70～521.1075°526.632.68503.10～550.10*76503.247.18469.45～536.9577496.733.45472.77～520.6378504.843.52473.67～535.9379490.258.07448.67～531.7380486.626.60467.57～505.6381506.128.48485.72～526.4882513.729.28492.75～534.6583481.529.78460.19～502.8184491.244.73459.22～523.1885515.725.78497.26～534.1486513.964.62467.69～560.1187496.423.82479.37～513.4388507.445.14475.10～539.7089479.144.15465.52～528.6890498.930.16477.32～520.4891503.753.90465.16～542.2492495.930.86473.78～518.0293494.658.48452.78～536.4294507.142.44476.74～537.4695488.536.15462.65～514.3596489.168.01440.44～537.7697°530.158.72488.09～572.1198518.745.10486.44～550.9699507.841.87477.85～537.73100540.655.17465.13～544.07

已知按正态分布，理论上有95%的变量值分布在均数加、减1.96倍标准差（样本均数的标准差称标准误）的范围内，这里也即100个样本均数中有95个分布在500－1.96(13.60)=473.34至500+1.96(13.60)=526.66的范围内。现看表6.4，在100个样本均数中，第6号（546.7）、第72号（465.3）、第97号(530.1)在上述范围之外，第42号(526.4)及第75号(526.6)就在临界值附近，其余95个（若将第42及75号计算在内则为97个）样本均数在此范围之内，将实际分布与理论分布相对照见下表6.5。100个样本均数的实际分布与正态分布的理论基本符合。