Datos: 100

Orden: De menor a mayor

19,65 20,18 20,21 20,22 20,23

20,23 20,25

20,28 20,31 20,31

20,33 20,35 20,37 20,4 20,41

20,42 20,45

20,48 20,5 20,53

20,57 20,62 20,72 20,82 21,12

21,18 21,22

21,25 21,28 21,29

21,3 21,32 21,34 21,36 21,3821,4

2 21,4421,4

8 21,52 21,5221,5

2 21,52 21,55 21,62 21,6321,6

6 21,6922,1

4 22,18 22,2222,2

5 22,27 22,29 22,31 22,35 22,4 22,4522,4

8 22,55 22,5822,6

2 22,78 22,84 23,11 23,1423,2

5 23,3223,3

5 23,41 23,4523,4

8 23,48 23,49 23,49 23,4923,5

1 23,5323,6

2 23,68 23,7523,8

4 24,25 24,29 24,33 24,4424,5

1 24,5624,6

2 24,66 24,6824,7

2 24,86 25,28 25,31 25,3525,3

5 25,3525,3

8 25,43 25,5

R. poblacional = X max - X min

R. poblacional = 25,5 – 19,65

R. poblacional = 5.85

R. muestral = X max - X min

R. muestral = 23,75 – 21,52

R. muestral = 2,23

Cuadro de cálculo de medidas de dispersión. (Población)

Ploblacion (xi) µ Disperciones (xi-µ)

Cuadrado de las dispersiones

(xi-µ)2

Cuadrado de las variantes (xi)2

1 19,65 22,354 -2,7042 7,31269764 386,12252 20,18 22,354 -2,1742 4,72714564 407,23243 20,21 22,354 -2,1442 4,59759364 408,44414 20,22 22,354 -2,1342 4,55480964 408,84845 20,23 22,354 -2,1242 4,51222564 409,25296 20,23 22,354 -2,1242 4,51222564 409,25297 20,25 22,354 -2,1042 4,42765764 410,06258 20,28 22,354 -2,0742 4,30230564 411,27849 20,31 22,354 -2,0442 4,17875364 412,4961

10 20,31 22,354 -2,0442 4,17875364 412,496111 20,33 22,354 -2,0242 4,09738564 413,308912 20,35 22,354 -2,0042 4,01681764 414,122513 20,37 22,354 -1,9842 3,93704964 414,936914 20,4 22,354 -1,9542 3,81889764 416,1615 20,41 22,354 -1,9442 3,77991364 416,568116 20,42 22,354 -1,9342 3,74112964 416,976417 20,45 22,354 -1,9042 3,62597764 418,202518 20,48 22,354 -1,8742 3,51262564 419,430419 20,5 22,354 -1,8542 3,43805764 420,2520 20,53 22,354 -1,8242 3,32770564 421,480921 20,57 22,354 -1,7842 3,18336964 423,124922 20,62 22,354 -1,7342 3,00744964 425,184423 20,72 22,354 -1,6342 2,67060964 429,318424 20,82 22,354 -1,5342 2,35376964 433,472425 21,12 22,354 -1,2342 1,52324964 446,054426 21,18 22,354 -1,1742 1,37874564 448,592427 21,22 22,354 -1,1342 1,28640964 450,288428 21,25 22,354 -1,1042 1,21925764 451,562529 21,28 22,354 -1,0742 1,15390564 452,838430 21,29 22,354 -1,0642 1,13252164 453,264131 21,3 22,354 -1,0542 1,11133764 453,6932 21,32 22,354 -1,0342 1,06956964 454,542433 21,34 22,354 -1,0142 1,02860164 455,395634 21,36 22,354 -0,9942 0,98843364 456,249635 21,38 22,354 -0,9742 0,94906564 457,104436 21,42 22,354 -0,9342 0,87272964 458,8164

37 21,44 22,354 -0,9142 0,83576164 459,673638 21,48 22,354 -0,8742 0,76422564 461,390439 21,52 22,354 -0,8342 0,69588964 463,110440 21,52 22,354 -0,8342 0,69588964 463,110441 21,52 22,354 -0,8342 0,69588964 463,110442 21,52 22,354 -0,8342 0,69588964 463,110443 21,55 22,354 -0,8042 0,64673764 464,402544 21,62 22,354 -0,7342 0,53904964 467,424445 21,63 22,354 -0,7242 0,52446564 467,856946 21,66 22,354 -0,6942 0,48191364 469,155647 21,69 22,354 -0,6642 0,44116164 470,456148 22,14 22,354 -0,2142 0,04588164 490,179649 22,18 22,354 -0,1742 0,03034564 491,952450 22,22 22,354 -0,1342 0,01800964 493,728451 22,25 22,354 -0,1042 0,01085764 495,062552 22,27 22,354 -0,0842 0,00708964 495,952953 22,29 22,354 -0,0642 0,00412164 496,844154 22,31 22,354 -0,0442 0,00195364 497,736155 22,35 22,354 -0,0042 1,764E-05 499,522556 22,4 22,354 0,0458 0,00209764 501,7657 22,45 22,354 0,0958 0,00917764 504,002558 22,48 22,354 0,1258 0,01582564 505,350459 22,55 22,354 0,1958 0,03833764 508,502560 22,58 22,354 0,2258 0,05098564 509,856461 22,62 22,354 0,2658 0,07064964 511,664462 22,78 22,354 0,4258 0,18130564 518,928463 22,84 22,354 0,4858 0,23600164 521,665664 23,11 22,354 0,7558 0,57123364 534,072165 23,14 22,354 0,7858 0,61748164 535,459666 23,25 22,354 0,8958 0,80245764 540,562567 23,32 22,354 0,9658 0,93276964 543,822468 23,35 22,354 0,9958 0,99161764 545,222569 23,41 22,354 1,0558 1,11471364 548,028170 23,45 22,354 1,0958 1,20077764 549,902571 23,48 22,354 1,1258 1,26742564 551,310472 23,48 22,354 1,1258 1,26742564 551,310473 23,49 22,354 1,1358 1,29004164 551,780174 23,49 22,354 1,1358 1,29004164 551,780175 23,49 22,354 1,1358 1,29004164 551,780176 23,51 22,354 1,1558 1,33587364 552,720177 23,53 22,354 1,1758 1,38250564 553,660978 23,62 22,354 1,2658 1,60224964 557,904479 23,68 22,354 1,3258 1,75774564 560,742480 23,75 22,354 1,3958 1,94825764 564,062581 23,84 22,354 1,4858 2,20760164 568,345682 24,25 22,354 1,8958 3,59405764 588,0625

83 24,29 22,354 1,9358 3,74732164 590,004184 24,33 22,354 1,9758 3,90378564 591,948985 24,44 22,354 2,0858 4,35056164 597,313686 24,51 22,354 2,1558 4,64747364 600,740187 24,56 22,354 2,2058 4,86555364 603,193688 24,62 22,354 2,2658 5,13384964 606,144489 24,66 22,354 2,3058 5,31671364 608,115690 24,68 22,354 2,3258 5,40934564 609,102491 24,72 22,354 2,3658 5,59700964 611,078492 24,86 22,354 2,5058 6,27903364 618,019693 25,28 22,354 2,9258 8,56030564 639,078494 25,31 22,354 2,9558 8,73675364 640,596195 25,35 22,354 2,9958 8,97481764 642,622596 25,35 22,354 2,9958 8,97481764 642,622597 25,35 22,354 2,9958 8,97481764 642,622598 25,38 22,354 3,0258 9,15546564 644,144499 25,43 22,354 3,0758 9,46054564 646,684910

0 25,5 22,354 3,1458 9,89605764 650,25∑ 2235,4 0,00 265,716836 50236,7426

Cuadro de cálculo de medidas de dispersión. (Muestra)

Ploblacion (xi) µ Disperciones (xi-µ)

Cuadrado de las dispersiones (xi-

µ)2

Cuadrado de las variantes (xi)2

1 21,52 22,6625 -1,1425 1,30530625 463,11042 21,52 22,6625 -1,1425 1,30530625 463,11043 21,55 22,6625 -1,1125 1,23765625 464,40254 21,62 22,6625 -1,0425 1,08680625 467,42445 21,63 22,6625 -1,0325 1,06605625 467,85696 21,66 22,6625 -1,0025 1,00500625 469,15567 21,69 22,6625 -0,9725 0,94575625 470,45618 22,14 22,6625 -0,5225 0,27300625 490,17969 22,18 22,6625 -0,4825 0,23280625 491,9524

10 22,22 22,6625 -0,4425 0,19580625 493,728411 23,48 22,6625 0,8175 0,66830625 551,310412 23,48 22,6625 0,8175 0,66830625 551,310413 23,49 22,6625 0,8275 0,68475625 551,780114 23,49 22,6625 0,8275 0,68475625 551,780115 23,49 22,6625 0,8275 0,68475625 551,780116 23,51 22,6625 0,8475 0,71825625 552,720117 23,53 22,6625 0,8675 0,75255625 553,660918 23,62 22,6625 0,9575 0,91680625 557,904419 23,68 22,6625 1,0175 1,03530625 560,742420 23,75 22,6625 1,0875 1,18265625 564,0625∑ 453,25 0,00 16,649975 10288,4281

VARIANZA POBLACIONAL

A) PRIMER MÉTODO B) SEGUNDO MÉTODO

Ơ²=∑(Xi−µ) ²N Ơ²=∑X i

2−(∑Xi) ²N

N

Ơ²=265,716836100 = 2.65 Ơ²=50236,7426−(2235,4 ) ²100

100 =

2.66

DESVIACIÓN ESTANDAR DE LAS VARIANTES

A) PRIMER MÉTODO B) SEGUNDO MÉTODO

Ơ=√∑(Xi−µ)²N

Ơ=√∑ Xi2−(∑Xi) ²N

N

Ơ=√2,65 = 1,62 Ơ=√2,66= 1,63

DESVIACION ESTANDAR DE LOS PROMEDIOS

OU=√O ²N =√ 2,65100 =√0,0265=0,162

COEFICIENTE DE VARIACION POBLACIONAL

C.V=Ơµ x 100%

C.V= 1,6222,354 x 100% = 7,24%

VARIANZA POBLACIONAL

A) PRIMER MÉTODO

S2 =(Xi−x ) ²n−1

S2 =16,64997520−1 = 0,876

B) SEGUNDO MÉTODO

S² =∑X i2−

(∑Xi) ²n

n−1

S² =10288,4281−(453,25) ²20

20−1 =

S² = 0,876

DESVIACION ESTANDAR DE LAS VARIANTES

A) PRIMER METODO B) SEGUNDO METODO

S= √ (Xi−x )²n−1

S= √∑ Xi2−(∑Xi) ²n

n−1

S= √ 16,64997520−1 = 0,93 S= √ 10288,4281−(453,25) ²

2020−1

=

0,93

DESVIACION ESTANDAR DE LOS PROMEDIOS

S² =√ s ²n =√ 0,87620 =√0,101= 0,2092

COEFICIENTE DE VARIACION MUESTRAL

C.V=Sµ x 100%

C.V= 0,9322,6625 x 100% = 4,1%