《统计学原理(第六版)》计算题解答第三章 综合指标1． 见教材P427 2． %86.1227025232018=+++=产量计划完成相对数发3． %85.101%108%110%%(%)===计划为上年的实际为上年的计划完成程度指标劳动生产率计划超额1.85%完成4． %22.102%90%92(%)(%)(%)===计划完成数实际完成数计划完成程度指标一季度产品单位成本未完成计划，实际单位成本比计划规定数高2.22%5． %105%103% %%(%) 计划为上年的计划为上年的实际为上年的计划完成程度指标=∴=1.94% %94.101103%105%% 即计划规定比上年增长计划为上年的解得：== 6． 见教材P427 7． 见教材P428)/(2502500625000)/(2702500675000亩千克亩千克乙甲======∑∑∑∑f xf X x mm X在相同的耕地自然条件下，乙村的单产均高于甲村，故乙村的生产经营管理工作做得好。

但由于甲村的平原地所占比重大，山地所占比重小，乙村则相反，由于权数的作用，使得甲村的总平均单产高于乙村。

%.fx X 9103=⋅=∑∑平均计划完成程度10． 见教材P42811． %74.94963.09222.09574.03=⨯⨯=G X 12. (1)%49.51X %49.105 08.107.105.104.102.1 X 1624632121=-=⨯⨯⨯⨯=∑⋅⋅⋅⋅⋅⋅=G ff n f f G nX X X 平均年利率：平均本利率为：(2) %50.5 162%84%76%53%4%2X =⨯+⨯+⨯+⨯+==∑∑fXf)亩/283.3( 8.25275 251332562600275 组为30027530026002f d m f 1m S 2fX e M L 千克中位数所在=+=⨯-+=-∴==∑⋅--∑+=⎪⎪⎪⎭⎫⎝⎛)亩/(5.942 45.91275 25119)-(13384)-(133275d X M 84133211L 0千克=+=⨯++=⋅+=-∆+∆∆之间—在亩千克之间—在亩千克—众数所在组为325300Q )/(82.31282.12300 450460034f 3 2511938946003300250225Q )/(03.24203.17225 15046004f 25691034600225)300275(3311∴=+==⨯=⨯-⨯+=∴=+===⨯-+=∑∑Q Q (2)R=500-150=350(千克/亩))亩/41.84(60025102.14ff x x A.D.千克==∑∑-=(3))/(55.5225102.2250.1444-4.5642 252)600229(6002738.5d 2f )f d A -x (f f 2)d A -x (σ)/278(287.525600229A d f )f d Ax (x )亩/277.96(600166775f xf x 亩千克亩千克或千克=⨯=⨯=⨯--=⨯⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡∑∑-∑∑==+⨯-=+⋅∑∑-===∑∑=“标准差”不要求用组距数列的简捷法计算 (4) 根据以上计算，294.5千克/亩>283.3千克/亩>277.96千克/亩，故资料分布为左偏(即下偏)。

14.(1)。

乙单位工人生产水平高人件人件乙甲乙甲∴<======∑∑∑∑ 8110018051200300X X )/(.xm m X )/(.f xf X(2) 齐乙单位工人生产水平整，人）件人件乙甲乙乙乙甲甲甲乙甲∴>=⨯=⨯==⨯=⨯====-====-=∑∑∑∑ V V %3.33%1008.16.0%100x σV %7.44%10050.167.0%100x σV /0.60(0.3610036ff)x (x σ)/0.67(0.4520090f f)x (x σ2212．其分布态势为左偏分布元)(550)7006003(21)3(210=-⨯⨯=-=M M X e第四章 动态数列1. 见教材P4302. 见教材P4303. 见教材P4314. 见教材P4325.(1) 见教材P433(2) ① 增减速度＝发展速度－1(或100%)② 0n 1i i a an 1i a a =∏=- (环比发展速度的连乘积等于定基发展速度) ③ 100%1基期发展水平的绝对值增长=④ 增减速度增减量的绝对值增长=%1⑤ 0n 1i i a a n1i )a (a -=∑=-- (逐期增减量之和等于累计增减量)⑥ n x x ∏= (平均发展速度等于环比发展速度的连乘积开n 次方)⑦ 平均增减速度=平均发展速度-1(或100%) 6. 见教材P433 7. 见教材P4339.17t 2214.03y 9.17b 2214.038990b 824053066421 tb t ty tb N yc 2+=∴⎩⎨⎧==∴⎩⎨⎧==⇒⎪⎩⎪⎨⎧+=+=∑∑∑∑∑a a a a 代入方程组：(2) ⎪⎩⎪⎨⎧+==+=⇒⎪⎪⎩⎪⎪⎨⎧++=++=++=∑∑∑∑∑∑∑∑∑∑∑708c 6010095460b727260c 914673 t c t b t y t t c t b t ty t c t b N y 4322322a a a a a 代入方程： 2c 10.2t 121.2t 1562.5y 2.102.1211562.5 ++=∴⎪⎩⎪⎨⎧===∴c b a (3)当t=5，即2004年基建投资额y c =1562.5+121.2×5+10.2×25=2423.5(万元)当t=6，即2005年基建投资额y c =1562.5+121.2×6+10.2×36=2656.9(万元)(2)代入方程组：t(1.21)36.3c y 21.13.36 08192.0lg 55982.1lg 10B 0.81925A 7.7991 2tB t A ty'tB NA y'⨯=∴⎩⎨⎧==⎩⎨⎧====∴⎩⎨⎧==⇒⎪⎩⎪⎨⎧∑+∑=∑∑+=∑b a b B a A 查反对数表得 (3)当t=3时，即该地区2004年底人口数为： lgy c =lga+tlgb=1.55982+3×0.08192=1.80558 ∴y c =63.9(万人)11.方法同上P43612.P436 其他略.不考第五章 统计指数1. (1)%04.11315.13.1q q %76.1118.66.7p p%83.9520.115.1q q %67.10682.192.1p p%77.12346.452.5q q %91.1102.244.2p p%1040.52.5q q %33.13330.040.0p p 0101010101010101====================水产品个体销售量指数水产品个体物价鲜蛋个体销售量指数鲜蛋个体物价猪肉个体销售量指数猪肉个体物价蔬菜个体销售量指数蔬菜个体物价(2)%60.115292.21614.24k %28.112614.246368.27k 0001q 1011p ==∑∑===∑∑=p q p q q p q p(3))(0228.3614.246368.2704.13.1)8.66.7()(138.015.1)80.192.1()(3248.152.5)2.244.2()(52.02.5)30.040.0()(111101101101101元=-=-=⨯-=⨯-=⨯-=⨯-=⨯-=⨯-=⨯-=⨯-∑∑qp q p q p p q p p q p p q p p2. P4393. P439)(02.5098.699750k 1%15.107%160.108120%670.106330%270.107300120330300 k 1k 1111111111111p万元=-=-=++++==⋅=∑∑∑∑∑∑p q p q pq p q pq p pp q4.)(8.66019488.2608qkp %92.13319488.2608700848400700%140848%110400%174q kp k 000000q 万元=-=-==++⨯+⨯+⨯==∑∑∑∑q p q p 5-7P4408.万元万元万元％％指数体系：（万元）产量指数（万元）（万元）总产值由于价格变化而增加的7235107 %6.10990.10497.114 357157501%90.1047157501107715822%97.11471582272750822%6.10975082200110011001100111011+=⨯==-=-===-=-===-==∑∑∑∑∑∑∑∑∑∑q p q p K q p q p K q p q p q p q p qp9-10. 略%56.111 %5%6.112%7%3.128%8%108%3%2.105 %3%98%10%7.109%16%4.116%48%63.109k %63.109 %14%1.108%13%3.102%48%08.117%25%100%100%2%100%98%100%08.117 %7%103%5%6.98%21%2.140%38%7.122 %4%7.101%17%7.96%2%100%6%1.106kw p =⨯+⨯+⨯+⨯+⨯+⨯+⨯+⨯==⨯+⨯+⨯+⨯==⨯+⨯==⨯+⨯+⨯+⨯+⨯+⨯+⨯+⨯==∑总指数食品类物价指数粮食类指数副食品指数 11. 产量总指数（万元）－加：由于价格变化使产值增价格总指数万元产值：由于产量增加而增加的75.01%29.10025.26126225.26115032801)(78.19%19.10847.24125.261 %5.10826298.015000.13205.1801111111110001000111110001===++===-==÷++=÷==∑∑∑∑∑∑∑∑∑∑∑∑q p kq p qp k qp K p q p q q p q p q p q p k p q p q K ppp q12.(1)参见教材P209-210的计算方法(2)%24.10365.067,368000,380%6.98000,10%5.102000,40%4.105000,30%4.108000,50%38.102000,30%35.101000,10%36.99000,15%23.101000,35%23.104000,20%11.105000,50%41.101000,90000,10000,40000,30000,50000,30000,10000,15000,35000,20000,50000,90k 1k 1111p ==++++++++++++++++++++=∑∑=q p q p 总指数13.(1)销售量指数%10335%103350001000010=⨯=⨯==q p q q q p q p q p K q (2)价格指数%96.110%10335401011=⨯==q p q p K p (3)销售量变动对销售额的影响)(05.1)1%103(35)(010万元=-⨯=-q q p14. 略%735.109 %25%118%35%5.108%29%104%11%110 )(=⨯+⨯+⨯+⨯=⋅=∑∑W Wk K p p15.商品销售量指数%65.11160.8602.9 %10329.189.989.901110110001==÷-=÷==∑∑∑∑∑∑pq p q p q p q p q p q K q由于销售量变动使商品销售额增加 9.602-8.60=1.002(亿元)16.(1) 以t 代表工人劳动生产率，q 代表工人人数149.251.8200 ; 129.48%111.56%144.44% )(2.149714)640450714650()q t -(t %130640450714650t t )(8.51640450)640714()t q -(q %56.111640714q q )(200450650q t q t %44.144450650q t q t 101010010100110011+=⨯=∴=⨯-==÷==⨯-====-=-===万元绝对值产值的影响：程度工人劳动生产率变动对万元绝对值度动对产值变动影响：程其中：生产工人人数变万元总产值指数(2) 以m 代表产值，q 代表职工数，t 代表生产工人人数)200(450-650)m -(m %44.144450650m m 0101万元产值指数=====其中：①职工人数变动影响：)22.4(t mq t )q (q %105800840q q 00000101的产值职工人数比重基期平均每个生产工人基期生产工人占万元↓↓=⨯⨯-==② 生产工人占职工人数比重变动影响： 值基期每个生产工人的产万元 )29.4(640450)800640840714(840t m )q t q t (q 106.25%800640840714q t q t 00001110011↓=⨯-⨯=⨯-⨯=÷=÷ ③ 由于工人劳动生产率变动对总产值的影响： 149.9429.422.4200 ; 130%106.25%105%144.44% 149.94)640450714650(840714840)t m t m (q t q 130%640450714650t m t m 00111110011++=⨯⨯=∴=-⨯⨯=-⨯⨯=÷=÷17.)33.76(-3.65-97.3559.94 96.7699.65110.28106.33 )(76.336.104084.1006p m q p m q %76.966.104084.1006p m q p m q )(65.325.10446.1040p m q p m q %65.9925.10446.1040p m q p m q )(35.979.94625.1044p m q p m q %28.1109.94625.1044pm q p m q )(94.599.94684.1006p m q p m q %33.1069.94684.1006p m q p m q 01111111111001111110011111111元＝％％％％＝元绝对数：响：每吨原材料价格变动影元绝对数：动影响：每吨产品原材料消耗变元绝对数：产量变动影响：元绝对数：原材料费用总额指数⨯⨯∴-=-=-==-=-=-===-=-===-=-===∑∑∑∑∑∑∑∑∑∑∑∑∑∑∑∑第六章 抽样调查1. (1)N=5000,000 n=500819339991841747233 4725002155472000500050015002155121554926X 222.X . ..t μ Δt .. μ.),(.)N n (n σμ. σ.f xfx x x ≤≤=⨯======-⨯=-===∑∑=(2) 0.68%0.12% 0.00680.00120.00280.0040.00280.0040.00280.00281t μΔ0.002850099.6%0.4%μ 0.0028)5000,000500(150099.6%0.4%μ6994040140140≤≤≤≤+≤≤-=⨯===⨯==-⨯=⨯=⨯==P P P %.%.%).-(%.-p)% p(.p p p 即2. (1)%9892% 3%95%3%-95% %303.0015.02 2t %45.95)(015.020005.095.0)1(%95200190≤≤+≤≤∆+≤≤∆-==⨯=⋅=∆===⨯=-===P P p P p t t F n p p P pp p p p μμ由(2)%82% 3%5%3%-5% %303.0015.02 2t %45.95)(015.020095.005.0)1(%505.020010≤≤+≤≤∆+≤≤∆-==⨯=⋅=∆===⨯=-====P P p P p t t F n p p P pp p p p μμ由3. (1)%5.74.5% %5.16%1.5%-6% %5.1%5.11 1t %27.68)(%5.1015.025094.006.0)1(%606.025015≤≤+≤≤∆+≤≤∆-=⨯=⋅=∆====⨯=-====P P p P p t t F n p p P pp p p p μμ由 (2)%P % %%P %%- Δp P Δ p %%.μt t F p p p p 9336363512 2 t %45.95)(≤≤+≤≤+≤≤-=⨯=⋅=∆==由4.34.91831.742 1.5880.7942t μΔ 0.794900566.7μ566.7300600300306002033.33300600300366003222222≤≤=⨯======+⨯+⨯=∑∑==+⨯+⨯=∑∑=X x n x f f σfXf X ii i σσ5. pp N 1000,000 n 1000 p 2% t 3μ0.004422%0.004423P 2%0.0044230.68%P 3.32%=======-⨯≤≤+⨯≤≤ 6. 98.83%F(t) 5034925160794731705160 3.79471012 51795160 1012 170 22===⨯=-===≤≤===查表得：已知：. t ..-t .t μx n σ μ.x . n σx x x7.2112222222222xf 32000x 800 σ141.42 σ20000f40xf 39500x 658.33 σ123.88 σ15347.22f60200004015347.2260σ17208.334060Nt σ100,000217208.33n N Δt σ100,0001∑=====∑∑=====∑⨯+⨯==+⋅⨯⨯==⋅+⋅⨯元元22304.99305(5217208.33==+⨯人)(1) 随机抽样：222222222xf 71500x 715f 100σ22025Nt σ100,000222025n 390.02391(N Δt σ100,00015222025====⋅⨯⨯====⋅+⋅⨯+⨯∑∑人)(2)29999150537011501153912202522=====⨯=⋅==...μΔt .n σt t μΔx8..n )x (x σ)x , x , x , x , x (m .r x x ri i673232596445403323188315454033231821215432121=++=∑-=======++++=∑==423918246278132813110031001544811051051610211161025831458314083133831238311844867104566734146732511 671043169114456310046467343364641431612522222221221222525242423232222.X ...t μΔ... N n N n R r R r δμ.).().().().().( r)x x (δ.)...(σr .n )x (x σn )x (x σ.n )x (x σn )x (x σx x ri i r i i ≤≤=⨯===--⨯+--⨯=--⋅+--⋅==-+-+-+-+-=∑-=∑=++++⨯=⋅==++=∑-==++=∑-==++=∑-==++=∑-===σσ均误差为：两个阶段抽样的抽样平各群群间方差：：各群群间方差的平均数9.(7849 32601150326011503260163021630984000270501144024144024649101)(6491024578415)(115024612022122千克千克即千克千克X ...X .-. ..t μΔ....)R r R (r δμ..rr )x (x δ..rxr x x x x x ri i x +≤≤∴=⨯===⨯=--⨯=--===∑∑-===∑∑==%.P %.%.%.P %.%-. %.%.t μΔ%...μ%..rr p)(p δ%.rr p p p p p ri i p i 05980797 494056974940569749402470224709840024000153001530240036770569724122≤≤+≤≤∴=⨯===⨯===∑∑-===∑∑==即10.(1))88(0.0152%98%10.01962%)-(12%) -(1 0.015 12块=⨯⨯==⨯==∆=n p p t (2) )(220.032%98%2块=⨯=n11. (1)小时。