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Ufumbuzi - Takwimu

Jumla:

2, 022

2,022

Kiwango cha kati:

x ̄ = 32.613

x̄=32.613

Kiwango cha kati:

32.5

32.5

Makazi:

71

Mabadiliko:

s^{2} = 368.438

s^2=368.438

Kipimo cha kawaida:

s = 19.195

s=19.195

Tazama hatua

Maelezo kwa hatua

1. Pata jumla

Jumlisha idadi zote:

$45 + 44 + 42 + 41 + 40 + 39 + 38 + 37 + 36 + 35 + 34 + 33 + 32 + 71 + 31 + 30 + 29 + 28 + 26 + 25 + 24 + 23 + 22 + 21 + 18 + 15 + 12 + 11 + 10 + 9 + 8 + 6 + 5 + 4 + 3 + 2 + 43 + 27 + 20 + 19 + 17 + 16 + 14 + 7 + 1 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 68 + 69 + 70 + 72 = 2022$

Jumla inafanana na $2, 022$

2. Pata wastani

Gawa jumla kwa idadi ya vigezo:

Jumla
$2, 022$
Idadi ya vigezo
$62$

$x ̄ = \frac{1011}{31} = 32.613$

Wastani unafanana na $32.613$

3. Pata kipimo cha katikati

Panga idadi kwa mpangilio unaozidi:
1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,44,45,45,46,47,48,49,50,51,52,53,54,55,56,68,69,70,71,72

Hesabu idadi ya istilahi:
Kuna (62) istilahi

Kwa sababu kuna idadi sawa ya istilahi, tambua istilahi mbili za kati:
1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,44,45,45,46,47,48,49,50,51,52,53,54,55,56,68,69,70,71,72

Pata thamani iliyo katikati ya istilahi mbili za kati kwa kuziweka pamoja na kugawa kwa 2:
$(32 + 33) / 2 = 65 / 2 = 32.5$

Kiwango cha kati ni sawa na 32.5

4. Pata mraba

Ili kupata mraba, toa thamani ndogo kutoka kwa thamani kubwa.

Thamani kubwa inafanana na 72
Thamani ndogo inafanana na 1

$72 - 1 = 71$

Makazi hulingana na 71

5. Pata tofauti

Ili kupata tofauti ya sampuli, pata tofauti kati ya kila kigezo na wastani, pata mraba wa matokeo, jumlisha matokeo yote ya mraba, na gawa jumla kwa idadi ya vigezo ikipunguzwa na 1.

Wastani unafanana na 32.613

Ili kupata tofauti za mraba, toa wastani kutoka kwa kila istilahi na mraba matokeo:

${(45 - 32.613)}^{2} = 153.440$

${(44 - 32.613)}^{2} = 129.666$

${(42 - 32.613)}^{2} = 88.118$

${(41 - 32.613)}^{2} = 70.343$

${(40 - 32.613)}^{2} = 54.569$

${(39 - 32.613)}^{2} = 40.795$

${(38 - 32.613)}^{2} = 29.021$

${(37 - 32.613)}^{2} = 19.247$

${(36 - 32.613)}^{2} = 11.472$

${(35 - 32.613)}^{2} = 5.698$

${(34 - 32.613)}^{2} = 1.924$

${(33 - 32.613)}^{2} = 0.150$

${(32 - 32.613)}^{2} = 0.376$

${(71 - 32.613)}^{2} = 1473.569$

${(31 - 32.613)}^{2} = 2.601$

${(30 - 32.613)}^{2} = 6.827$

${(29 - 32.613)}^{2} = 13.053$

${(28 - 32.613)}^{2} = 21.279$

${(26 - 32.613)}^{2} = 43.730$

${(25 - 32.613)}^{2} = 57.956$

${(24 - 32.613)}^{2} = 74.182$

${(23 - 32.613)}^{2} = 92.408$

${(22 - 32.613)}^{2} = 112.634$

${(21 - 32.613)}^{2} = 134.860$

${(18 - 32.613)}^{2} = 213.537$

${(15 - 32.613)}^{2} = 310.214$

${(12 - 32.613)}^{2} = 424.892$

${(11 - 32.613)}^{2} = 467.118$

${(10 - 32.613)}^{2} = 511.343$

${(9 - 32.613)}^{2} = 557.569$

${(8 - 32.613)}^{2} = 605.795$

${(6 - 32.613)}^{2} = 708.247$

${(5 - 32.613)}^{2} = 762.472$

${(4 - 32.613)}^{2} = 818.698$

${(3 - 32.613)}^{2} = 876.924$

${(2 - 32.613)}^{2} = 937.150$

${(43 - 32.613)}^{2} = 107.892$

${(27 - 32.613)}^{2} = 31.505$

${(20 - 32.613)}^{2} = 159.085$

${(19 - 32.613)}^{2} = 185.311$

${(17 - 32.613)}^{2} = 243.763$

${(16 - 32.613)}^{2} = 275.989$

${(14 - 32.613)}^{2} = 346.440$

${(7 - 32.613)}^{2} = 656.021$

${(1 - 32.613)}^{2} = 999.376$

${(44 - 32.613)}^{2} = 129.666$

${(45 - 32.613)}^{2} = 153.440$

${(46 - 32.613)}^{2} = 179.214$

${(47 - 32.613)}^{2} = 206.989$

${(48 - 32.613)}^{2} = 236.763$

${(49 - 32.613)}^{2} = 268.537$

${(50 - 32.613)}^{2} = 302.311$

${(51 - 32.613)}^{2} = 338.085$

${(52 - 32.613)}^{2} = 375.860$

${(53 - 32.613)}^{2} = 415.634$

${(54 - 32.613)}^{2} = 457.408$

${(55 - 32.613)}^{2} = 501.182$

${(56 - 32.613)}^{2} = 546.956$

${(68 - 32.613)}^{2} = 1252.247$

${(69 - 32.613)}^{2} = 1324.021$

${(70 - 32.613)}^{2} = 1397.795$

${(72 - 32.613)}^{2} = 1551.343$

Ili kupata mabadiliko ya sampuli, ongeza tofauti za mraba na ugawe jumla yao kwa idadi ya istilahi minus 1

Jumla:
$153.440 + 129.666 + 88.118 + 70.343 + 54.569 + 40.795 + 29.021 + 19.247 + 11.472 + 5.698 + 1.924 + 0.150 + 0.376 + 1473.569 + 2.601 + 6.827 + 13.053 + 21.279 + 43.730 + 57.956 + 74.182 + 92.408 + 112.634 + 134.860 + 213.537 + 310.214 + 424.892 + 467.118 + 511.343 + 557.569 + 605.795 + 708.247 + 762.472 + 818.698 + 876.924 + 937.150 + 107.892 + 31.505 + 159.085 + 185.311 + 243.763 + 275.989 + 346.440 + 656.021 + 999.376 + 129.666 + 153.440 + 179.214 + 206.989 + 236.763 + 268.537 + 302.311 + 338.085 + 375.860 + 415.634 + 457.408 + 501.182 + 546.956 + 1252.247 + 1324.021 + 1397.795 + 1551.343 = 22474.710$
Idadi ya istilahi:
$62$
Idadi ya istilahi minus 1:
61

Mabadiliko:
$\frac{22474.710}{61} = 368.438$

Mabadiliko ya sampuli ( $s^{2}$ ) ni sawa na 368.438

6. Pata kipimo cha kiwango cha kawaida

Kipimo cha kiwango cha kawaida cha sampuli kinatokana na mraba wa tofauti ya sampuli. Hii ndio sababu tofauti mara nyingi huwakilishwa na kigezo kilichopigwa mraba.

Tofauti: $s^{2} = 368.438$

Pata kisquere ukiwa:
$s = \sqrt{(368.438)} = 19.195$

Kipimo cha kawaida ( $s$ ) ni sawa na 19.195

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