统计学原理作业.doc

1.(1) 表1 我国19952009年国内生产总值情况一览表年份国内生产总值（亿元）逐期增长量（亿元）累计增长量（亿元）199560793.7199671176.610382.910382.91997789737796.418179.3199884402.35429.323608.6199989677.15274.828883.4200099214.69537.538420.92001109655.210440.648861.52002120332.710677.5595392003135822.815490.175029.12004159878.324055.599084.62005184937.425059.1124143.72006216314.431377155520.72007265810.349495.9205016.62008314045.448235.1253251.72009340506.926461.5279713.2年平均增长量：19979.514（2）表2 我国19952009年国内生产总值情况一览表年份国内生产总值环比发展速度环比增长速度定基发展速度定基增长速度199560793.7199671176.61.1707890780.1707890781.1707890780.1707890781997789731.1095359990.1095359991.299032630.29903263199884402.31.0687488130.0687488131.3883395810.388339581199989677.11.0624959270.0624959271.4751051510.475105151200099214.61.1063537960.1063537961.6319881830.6319881832001109655.21.1052324960.1052324961.8037263730.8037263732002120332.71.0973734030.0973734031.9793613480.9793613482003135822.81.128727270.128727272.2341591321.2341591322004159878.31.177109440.177109442.6298498041.6298498042005184937.41.1567385940.1567385943.0420487652.0420487652006216314.41.1696628160.1696628163.5581713242.5581713242007265810.31.2288146330.2288146334.3723329883.3723329882008314045.41.1814643750.1814643755.1657556624.1657556622009340506.91.084260110.084260115.6010228034.601022803（3）水平法求年平均发展速度（几何平均）： X=14340506.9/60793.7=1.130961099 累计法求年平均发展速度（方程法）： X+X2+X14=37.35168282(定基发展速度之和)求得：X=1.1235158水平法求年平均增长速度： X=平均发展速度-1=0.130961099累计法求年平均增长速度： X=0.12351582.（1）根据趋势图和数据看，该时序数列本期金额较上年同期有所增加，且每年各个月份金额变化不大。（2）用移动平均法求趋势值表3 某外销公司订单金额趋势值表年份 月份20062007200820092010合计月平均数季节比率1 -54.63858.72565.01769.858248.23862.05941.001132 -54.83859.27965.31770.267249.762.4251.007033 -55.00859.92565.60870.621251.16362.79061.012934 -55.41360.38366.13870.821252.75463.18851.019355 -55.95860.74266.72971.025254.45463.61351.026216 -56.29261.29667.21771.246256.0564.01251.03264754.57556.7561.96367.313 -240.660.150.97033854.51757.13362.38867.796 -241.83360.45830.97531954.53857.362.75468.771 -243.36360.84060.981471054.41357.52163.45469.113 -244.561.1250.986061154.53357.74264.18369.317 -245.77561.44380.99121254.658.17564.64669.625 -247.04661.76150.99633合计 - - - - -2975.48 -12总平均数 - - - - - -61.9891 -（3） yc=a+bt， y=naty=bt2 表4 某公司外销金额直线趋势方程计算表年份 t y tyt2yc2006-2657.5-13154642.022007-1677.2-677.21695.0420080739.700748.0620091809.4809.41801.0820102856.517134854.1合计 -3740.3530.2103740.3 y=3740.3 ty=530.2 t2=10代入上列联立方程组中，得 3740.3=5a530.2=10b所以a=3740.3/5=748.06， b=530.2/10=53.02将a、b值代入直线方程式，得 yc=748.06+53.02t则：yc（2011）=748.06+53.02*