taller de estadistica umng

Xi ni Ni f1000 2 2 4.00%1110 2 4 4.00%1123 6 10 12.00%1145 2 12 4.00%1156 2 14 4.00%1167 2 16 4.00%1200 4 20 8.00%1234 4 24 8.00%1248 4 28 8.00%1347 2 30 4.00%1445 2 32 4.00%1446 2 34 4.00%1455 2 36 4.00%1456 2 38 4.00%1458 2 40 4.00%1520 2 42 4.00%1556 2 44 4.00%1920 4 48 8.00%2000 2 50 4.00%

N= 50

Mo = > ni 1123

1248 25

1353.36

RANGO= Xi max. - Xi min. 1000

Me = Ni≥ N/2

MEDIA ( X ) = ∑Xi*Fi

Fi4.00% 40.00 -706.728.00% 44.40 -486.7220.00% 134.76 -1382.1624.00% 45.80 -416.7228.00% 46.24 -394.7232.00% 46.68 -372.7240.00% 96.00 -613.4448.00% 98.72 -477.4456.00% 99.84 -421.4460.00% 53.88 -12.7264.00% 57.80 183.2868.00% 57.84 185.2872.00% 58.20 203.2876.00% 58.24 205.2880.00% 58.32 209.2884.00% 60.80 333.2888.00% 62.24 405.2896.00% 153.60 2266.56

100.00% 80.00 1293.281353.36 0

DM=(Xi-X)* ni / N = 0

69443.4304

Desv est. (S)= raiz^2 de (S^2) 263.5212143263

coef. Varia (C.V.) = (D.S / X)*100% 19.47

X=∑Xi*f DM=∑(Xi-X)*ni / N

VARI (S^2) = (∑(Xi-X)^2*ni)/N

(S^2) = (∑(Xi-X)^2*ni)/N

249726.58118448.18318394.3886827.7877901.9469460.1094077.1656987.2444402.92

80.9016795.7817164.3420661.3821069.9421899.0655537.7882125.94

1284323.56836286.58

3472171.52

%

Xi ni Ni f43.6 3 3 2.50%45 6 9 5.00%

45.3 6 15 5.00%45.6 3 18 2.50%45.8 6 24 5.00%45.9 3 27 2.50%46.3 3 30 2.50%46.5 3 33 2.50%46.7 3 36 2.50%46.9 6 42 5.00%47.1 6 48 5.00%47.2 3 51 2.50%47.3 3 54 2.50%47.4 6 60 5.00%47.8 3 63 2.50%47.9 3 66 2.50%48.1 3 69 2.50%48.2 3 72 2.50%48.3 6 78 5.00%48.4 9 87 7.50%48.9 3 90 2.50%49.1 9 99 7.50%49.2 3 102 2.50%49.5 3 105 2.50%49.6 3 108 2.50%49.8 3 111 2.50%50 9 120 7.50%

N = 120

Mo = > ni120 60

47.56

RANGO= Xi max. - Xi min. 6.4

45.3 45 46.9 45.845 43.6 46.7 47.9

48.4 48.9 47.3 46.947.4 48.4 49.1 45.649.6 50 50 47.845.9 47.2 48.2 49.146.3 47.4 48.3 49.149.5 48.4 48.3 49.245.3 45 46.9 45.845 43.6 46.7 47.9

Me = Ni≥ N/2MEDIA ( X ) = ∑Xi*Fi

48.4 48.9 47.3 46.947.4 48.4 49.1 45.649.6 50 50 47.845.9 47.2 48.2 49.146.3 47.4 48.3 49.149.5 48.4 48.3 49.245.3 45 46.9 45.845 43.6 46.7 47.9

48.4 48.9 47.3 46.947.4 48.4 49.1 45.649.6 50 50 47.845.9 47.2 48.2 49.146.3 47.4 48.3 49.149.5 48.4 48.3 49.2

Fi2.50% 1.09 -11.877.50% 2.25 -15.3312.50% 2.27 -13.5315.00% 1.14 -5.8620.00% 2.29 -10.5322.50% 1.15 -4.9625.00% 1.16 -3.7627.50% 1.16 -3.1630.00% 1.17 -2.5635.00% 2.35 -3.9340.00% 2.36 -2.7342.50% 1.18 -1.0645.00% 1.18 -0.7650.00% 2.37 -0.9352.50% 1.20 0.7455.00% 1.20 1.0457.50% 1.20 1.6460.00% 1.21 1.9465.00% 2.42 4.4772.50% 3.63 7.6175.00% 1.22 4.0482.50% 3.68 13.9185.00% 1.23 4.9487.50% 1.24 5.8490.00% 1.24 6.1492.50% 1.25 6.74

100.00% 3.75 22.01

X = 47.56 0.00

0.00

$ 2.58

Desv est. (S)= raiz^2 de (S^2) $ 1.61

coef. Varia (C.V.) = (D.S / X)*100% 3.38

47.147.145.848.145.3

5049.846.547.147.1

X=∑Xi*f DM=∑(Xi-X)*ni / N

DM=∑(Xi-X)* ni / N =

VARI (S^2) = ((∑Xi-X)^2*ni)/N

45.848.145.3

5049.846.547.147.145.848.145.3

5049.846.5

(S^2) = (∑(Xi-X)^2*ni)/N

$ 46.93$ 39.17$ 30.51$ 11.47$ 18.48$ 8.22$ 4.73 -81.00$ 3.34 81.00$ 2.19$ 2.57$ 1.24$ 0.38$ 0.20$ 0.14$ 0.18$ 0.36$ 0.89$ 1.25$ 3.33$ 6.43$ 5.43$ 21.48$ 8.12$ 11.35$ 12.55$ 15.12$ 53.80

$ 309.84

2.6036722689

%