1. Ejercicio 8
Estadística

2. 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20
1.402 1.504 1.502 1.496 1.482 1.522 1.495 1.478 1.506 1.489 1.441 1.477 1.516 1.466 1.582 1.500 1.450 1.592 1.530 1.587
1.517 1.519 1.522 1.500 1.526 1.450 1.509 1.508 1.501 1.483 1.484 1.471 1.470 1.464 1.490 1.494 1.465 1.493 1.484 1.505
1.484 1.534 1.476 1.479 1.510 1.516 1.467 1.478 1.493 1.525 1.508 1.488 1.476 1.490 1.526 1.492 1.460 1.483 1.515 1.492
1.479 1.479 1.475 1.483 1.495 1.547 1.555 1.491 1.514 1.493 1.500 1.523 1.466 1.492 1.499 1.502 1.490 1.474 1.456 1.431
1.450 1.518 1.452 1.519 1.553 1.511 1.497 1.516 1.519 1.514 1.507 1.534 1.514 1.525 1.539 1.489 1.448 1.502 1.570 1.522
1.467 1.509 1.473 1.508 1.532 1.470 1.519 1.516 1.488 1.496 1.448 1.540 1.473 1.526 1.592 1.472 1.543 1.528 1.516 1.498
1.392 1.514 1.458 1.455 1.484 1.468 1.489 1.450 1.501 1.485 1.480 1.478 1.467 1.532 1.487 1.512 1.478 1.542 1.469 1.475
1.540 1.486 1.479 1.522 1.406 1.488 1.513 1.598 1.447 1.504 1.505 1.507 1.514 1.506 1.489 1.493 1.471 1.482 1.490 1.503
1.547 1.548 1.481 1.514 1.509 1.544 1.486 1.444 1.514 1.464 1.466 1.514 1.434 1.468 1.498 1.461 1.510 1.528 1.521 1.516
1.487 1.491 1.499 1.505 1.519 1.542 1.486 1.496 1.485 1.505 1.448 1.463 1.496 1.471 1.530 1.510 1.514 1.516 1.543 1.548
1.478 1.522 1.508 1.523 1.509 1.515 1.577 1.509 1.506 1.505 1.521 1.494 1.500 1.497 1.510 1.484 1.507 1.451 1.501 1.511
1.538 1.468 1.506 1.408 1.418 1.508 1.532 1.482 1.518 1.495 1.520 1.463 1.562 1.488 1.538 1.485 1.497 1.489 1.504 1.452
1.437 1.511 1.515 1.493 1.447 1.571 1.516 1.481 1.515 1.488 1.446 1.510 1.527 1.457 1.518 1.551 1.553 1.475 1.537 1.482
1.489 1.523 1.467 1.533 1.526 1.471 1.496 1.535 1.474 1.498 1.506 1.530 1.485 1.468 1.562 1.488 1.467 1.446 1.484 1.487
1.459 1.501 1.546 1.447 1.453 1.496 1.478 1.489 1.550 1.483 1.561 1.469 1.496 1.503 1.495 1.509 1.530 1.553 1.544 1.518

3. max 1.598 intervalos aparentes intervalos
reales
min 1.392 lim inf
lim sup lim inf lim sup xi fi fa fri frai fi*xi xi-ma*fi (xi-xtes)^2*fi
rango= 0.206 0.0133 0.0133 0.383946 0.0368
1.392 1.414 1.3915 1.4145 1.403 4 4 33 33 5.612 667 54
0.0133 0.0266 0.291946 0.0213
1.415 1.437 1.4145 1.4375 1.426 4 8 33 66 5.704 667 08
tam 0.0228 0.1066 0.0599
inter= 89 1.438 1.46 1.4375 1.4605 1.449 24 32 0.08 66 34.776 1.19968 68
0.1933 1.565226 0.0422
1.461 1.483 1.4605 1.4835 1.472 58 90 33 0.3 85.376 667 4
0.023 0.0014
1.484 1.506 1.4835 1.5065 1.495 90 180 0.3 0.6 134.55 0.3588 3
0.0271
1.507 1.529 1.5065 1.5295 1.518 75 255 0.25 0.85 113.85 1.426 13
0.0529
1.53 1.552 1.5295 1.5525 1.541 30 285 0.1 0.95 46.23 1.2604 54
0.0380
1.553 1.575 1.5525 1.5755 1.564 9 294 0.03 0.98 14.076 0.58512 41
0.0464
1.576 1.598 1.5755 1.5985 1.587 6 300 0.02 1 9.522 0.52808 78
449.69 0.3263
300 6 7.5992 86
media 1.4989
aritmetica= 87
desv 0.025330
media= 667
0.00108
varianza= 795
0.03298
desv estandar= 413

4. x y
1.3915 0
1.3915 4 120
1.4145 4 HISTOGRAMA
1.4145 0 100 media
1.4145 4
1.4375 4 x+s
1.4375 0 80
x+2s
1.4375 24
x+3s
1.4605 24 60
1.4605 0 x-s
1.4605 58
40 x-2s
1.4835 58
1.4835 0 x+3s
1.4835 90 20
tv
1.5065 90
1.5065 0 usl
0
1.5065 75
lsl
1.5295 75 1.3 1.4 1.5 1.6 1.7
1.5295 0
1.5295 30
1.5525 30
1.5525 0
1.5525 9
1.5755 9
1.5755 0
1.5755 6
1.5985 6
1.5985 0

5. x tv
x-s
1.498987 0 1.5 0
1.498987 100 1.466003 0
1.5 110
x+s 1.466003 100
1.531971 0
1.531971 100 x-2s
usl
x+2s 1.433019 0
1.35 0
1.564955 0
1.433019 100 1.35 110
1.564955 100
x-3s lsl
x+3s
1.597939 0 1.4000346 0 1.65 0
1.597939 100 1.4000346 100 1.65 110

6. 120
x+3s
HISTOGRAMA
100 media
x+s
80
x+2s
60 x+3s
x-s
40
x-2s
20 x+3s
tv
0
usl
1.3 1.4 1.5 1.6 1.7
tv
x-2s
x+3s 1.4 0
1.43301873 0 1.4 110
1.5979394 0
1.43301873 100
1.5979394 100
x-s
1.46600287 0 x-3s usl
1.4000346 0 1.55 0
1.46600287 100
1.55 110
1.4000346 100
lsl
1.55 0
1.55 110

7. 120
HISTOGRAMA
100 media
x+s
80
x+2s
60 x+3s
x-s
40
x-2s
20 x+3s
tv
0
usl
1.3 1.4 1.5 1.6 1.7
tv
1.45 0
1.45 110
usl
1.3 0
1.3 110
lsl
1.6 0
1.6 110

8. 120 x
HISTOGRAMA
100
1.498987 0
media
1.498987 100
x+s
80 x+s
x+2s
60
1.53197113 0
x+3s
1.53197113 100
x-s
40 x+2s
x-2s
20 x+3s
1.56495527 0
tv
1.56495527 100
0
usl
1.3 1.4 1.5 1.6 1.7 x+3s
1.5979394 0
tv 1.5979394 100
1.55 0 x-s
1.55 110 1.46600287 0
1.46600287 100
usl
x-2s
1.4 0
1.4 110
1.43301873 0
1.43301873 100
lsl
1.7 0 x-3s
1.7 110 1.4000346 0
1.4000346 100

9. 120
x
100 HISTOGRAMA 1.498987 0
media 1.498987 100
x+s
80 x+s
1.53197113 0
x+2s
1.53197113 100
60 x+3s
x+2s
x-s
1.56495527 0
40 x-2s 1.56495527 100
x+3s
20 tv x+3s
usl 1.5979394 0
0 lsl
1.5979394 100
x-s
1.3 1.4 1.5 1.6 1.7
1.46600287 0
1.46600287 100
tv
1.6 0 lsl x-2s
1.6 110 1.43301873 0
1.45 0
1.43301873 100
1.45 110
x-3s
usl 1.4000346 0
1.4000346 100
1.75 0
1.75 110

10. 120
x
1.498987 0
100 HISTOGRAMA
1.498987 100
media
x+s
80 x+s
1.53197113 0
x+2s
1.53197113 100
x+3s
60 x+2s
x-s
1.56495527 0
x-2s
1.56495527 100
40
x+3s
tv
x+3s
20 usl 1.5979394 0
lsl 1.5979394 100
0 tv x-s
1.46600287 0
1.3 1.4 1.5 1.6 1.7 1.4 0
1.4 110 1.46600287 100
usl x-2s
1.6 0 1.43301873 0
1.43301873 100
1.6 110
x-3s
lsl
1.4000346 0
1.2 0
1.4000346 100
1.2 110

11. 120
x
1.498987 0
HISTOGRAMA
100 1.498987 100
media
x+s
x+s
80 1.53197113 0
x+2s
1.53197113 100
x+3s
60 x+2s
x-s
1.56495527 0
x-2s
40 1.56495527 100
x+3s
tv
20 x+3s
usl
1.5979394 0
lsl
0 1.5979394 100
tv
1.3 1.4 1.5 1.6 1.7 x-s
1.45 0 1.46600287 0
1.45 110 1.46600287 100
usl x-2s
1.25 0 1.43301873 0
1.25 110 1.43301873 100
lsl x-3s
1.65 0 1.4000346 0
1.65 110 1.4000346 100

12. 120
x
1.498987 0
100 HISTOGRAMA
1.498987 100
media x+s
80 x+s 1.531971 0
x+2s 1.531971 100
x+2s
x+3s
60 1.564955 0
x-s
1.564955 100
x-2s
40
x+3s x+3s
tv 1.597939 0
20 usl 1.597939 100
x-s
lsl
1.466003 0
0 tv
1.466003 100
1.3 1.4 1.5 1.6 1.7 1.5 0
1.5 110 x-2s
1.433019 0
usl 1.433019 100
1.3 0
1.3 110 x-3s
1.4000346 0
1.4000346 100
lsl
1.7 0
1.7 110

13. 120
x
1.498987 0
100 HISTOGRAMA
1.498987 100
media
x+s
x+s
80 1.53197113 0
x+2s 1.53197113 100
x+3s x+2s
60
x-s 1.56495527 0
1.56495527 100
x-2s
40
x+3s
x+3s
tv
1.5979394 0
20
usl 1.5979394 100
lsl x-s
0 tv 1.46600287 0
1.46600287 100
1.3 1.4 1.5 1.6 1.7 1.55 0
1.55 110 x-2s
1.43301873 0
1.43301873 100
usl
1.35 0
x-3s
1.35 110 1.4000346 0
1.4000346 100
lsl
1.75 0
1.75 110

14. 120
x
100 HISTOGRAMA 1.498987 0
media 1.498987 100
x+s
x+s
80
1.53197113 0
x+2s
1.53197113 100
x+3s
60 x+2s
x-s
1.56495527 0
x-2s
40 1.56495527 100
x+3s
tv
x+3s
20
usl 1.5979394 0
lsl 1.5979394 100
0
tv x-s
1.3 1.4 1.5 1.6 1.7 1.46600287 0
1.6 0
1.46600287 100
1.6 110
usl x-2s
1.4 0 1.43301873 0
1.43301873 100
1.4 110
x-3s
lsl 1.4000346 0
1.8 0 1.4000346 100
1.8 110