x y

170 172 0
172 178 0
169 168 0
170 178 0
169 173 0
175 175 0
176 174 0
178 173 0
170 171 0
168 173 0
170 175 0
172 178 0

Diagram ro
166 168 170 172
výška [c
 Diagram rozptýlení
168 170 172 174 176 178 180
výška [cm]
 Absolutní Relativní Absolutní
Hodnoty
x četnost četnost [%] kumulativní
41 37 37 8 25% 8
39 37 38 3 9% 11
41 37 39 1 3% 12
37 37 40 6 19% 18
37 37 41 4 13% 22
42 37 42 4 13% 26
43 37 43 6 19% 32
39 37 ∑ 32 100%
41 38
41 38
43 38 Četnost
38 39 9
37 40
8 8
39 40
39 40 7

38 40 6 6

polynom četností
40 40
5
37 40
38 41 4

38 41 3 3
38 41
2
39 41
43 42 1 1
37 42 0
37 38 39 40
43 42
37 42 d [cm]
43 43 relativní četnost
kumulativní četnos
40 43
38 43
42 43
41 43
41 43
 Relativní Absolutní
kumulativní [%] kumulativní
25% 8
34% 11
38% 12
56% 18
69% 22
81% 26
100% 32

Četnost
35

30

25
6 6
součtová křivka
20

4 4 15
3
10

5
1

0
38 39 40 41 42 43

d [cm]
relativní četnost
kumulativní četnost
0.900115 0.754399 0.420193 0.77194 0.566202 0.481061 0.757002 0.503344 0.216434 0.816546
0.257126 0.334311 0.974392 0.474287 0.889071 0.925378 0.025109 0.690822 0.455243 0.277945
0.573404 0.373687 0.025041 0.070207 0.326233 0.334145 0.012145 0.377412 0.595683 0.945963
0.300896 0.130457 0.677368 0.569143 0.205453 0.776592 0.263979 0.057939 0.439855 0.48941
0.041672 0.189304 0.122422 0.848798 0.621613 0.159248 0.15329 0.449949 0.826514 0.937133
0.954456 0.780289 0.096645 0.191664 0.068517 0.988645 0.466925 0.348549 0.759239 0.413242
0.00024 0.479906 0.852805 0.059455 0.02784 0.29933 0.520111 0.855995 0.32571 0.567059
0.954925 0.733502 0.299524 0.018462 0.163058 0.570362 0.119037 0.159153 0.620193 0.132979
0.632397 0.092657 0.246094 0.164297 0.309084 0.753202 0.798552 0.741245 0.128355 0.58858
0.549135 0.873003 0.088998 0.790533 0.219169 0.018354 0.653593 0.118384 0.643735 0.737469
0.493476 0.96085 0.142821 0.594281 0.351812 0.466222 0.149383 0.879956 0.944875 0.514949
0.523745 0.41038 0.547591 0.499173 0.826882 0.379135 0.355444 0.988614 0.002104 0.865166
0.852847 0.454898 0.149552 0.943503 0.686835 0.472226 0.936551 0.362589 0.002781 0.356307
0.714157 0.826102 0.72564 0.794134 0.720039 0.622561 0.276215 0.420574 0.049725 0.559695
0.522472 0.190045 0.071523 0.120377 0.54963 0.589089 0.638382 0.264261 0.062085 0.508215
0.82406 0.002504 0.970189 0.090539 0.562992 0.046717 0.353672 0.036563 0.64149 0.641981
0.94191 0.661224 0.582188 0.823743 0.562527 0.683179 0.175278 0.237567 0.766661 0.578499
0.812346 0.336602 0.655053 0.908169 0.488371 0.530066 0.093301 0.721037 0.615151 0.230751
0.246818 0.923402 0.952515 0.301731 0.612419 0.06402 0.749427 0.981602 0.055633 0.265666
0.814802 0.684966 0.680006 0.572473 0.241958 0.27903 0.73064 0.479821 0.657434 0.10312
0.554274 0.432771 0.372518 0.638372 0.71575 0.474141 0.866122 0.389926 0.430818 0.725151
0.803302 0.119024 0.828305 0.984117 0.531556 0.573501 0.470124 0.044023 0.535537 0.364
0.459313 0.805717 0.627011 0.458317 0.672908 0.854441 0.580896 0.36136 0.239839 0.571785
0.279176 0.017287 0.317684 0.91898 0.266806 0.928849 0.940362 0.682268 0.908107 0.513786
0.68664 0.246296 0.936189 0.26601 0.090493 0.978124 0.604055 0.167252 0.635732 0.19851
0.196874 0.168326 0.846393 0.478531 0.732057 0.014139 0.135401 0.444877 0.671436 0.079675
0.039922 0.72063 0.464449 0.194448 0.712003 0.41851 0.125102 0.246844 0.126983 0.567747
0.099549 0.720622 0.126128 0.063887 0.036134 0.443343 0.833495 0.699202 0.970803 0.754092
0.244844 0.742896 0.849677 0.534585 0.349265 0.999105 0.393936 0.865565 0.442684 0.864423
0.73674 0.814515 0.503691 0.943214 0.236526 0.722477 0.863015 0.295369 0.60398 0.8598
0.748221 0.667856 0.642908 0.091356 0.297484 0.259886 0.060329 0.644554 0.715775 0.307958
0.696217 0.863294 0.38758 0.36737 0.873665 0.945383 0.385104 0.281046 0.209764 0.348474
0.445287 0.069724 0.661041 0.910623 0.839043 0.746911 0.104218 0.814719 0.579908 0.18461
0.092079 0.468284 0.842584 0.57283 0.555747 0.222945 0.243904 0.023755 0.748608 0.808369
0.625729 0.825421 0.39672 0.329819 0.051691 0.377874 0.202749 0.40802 0.190886 0.648499
0.734002 0.048479 0.133691 0.60402 0.00815 0.719189 0.16006 0.83584 0.559506 0.262302
0.622248 0.218013 0.712627 0.248875 0.134605 0.384383 0.09181 0.346407 0.06224 0.290165
0.826748 0.58033 0.265662 0.089936 0.570294 0.884695 0.27203 0.713488 0.585958 0.14582
0.730248 0.899502 0.736639 0.831993 0.499158 0.677741 0.922974 0.948196 0.30005 0.497968
0.504811 0.500741 0.038856 0.211405 0.836661 0.332241 0.844311 0.084193 0.435607 0.108975
0.943899 0.348423 0.850902 0.936775 0.224622 0.774578 0.837829 0.04398 0.364547 0.875979
0.949685 0.502986 0.91119 0.162983 0.31312 0.145209 0.517419 0.196907 0.655766 0.798711
0.586198 0.486226 0.437403 0.729995 0.242514 0.955247 0.512276 0.14601 0.092506 0.32387
0.097203 0.057661 0.490782 0.842464 0.165561 0.673642 0.580521 0.597877 0.164152 0.975606
0.766302 0.320729 0.759679 0.312115 0.776511 0.561414 0.196599 0.42212 0.719319 0.297542
0.384661 0.820093 0.543161 0.474257 0.012789 0.907516 0.703654 0.671825 0.769389 0.59048
0.671717 0.590476 0.351807 0.930468 0.243019 0.882329 0.780247 0.469626 0.806183 0.314142
0.652409 0.949188 0.911993 0.807428 0.925753 0.761543 0.506086 0.527269 0.486158 0.706472
0.144776 0.073563 0.381363 0.830867 0.280325 0.022615 0.748744 0.468736 0.744119 0.493007
0.484813 0.801359 0.85173 0.153574 0.461892 0.948044 0.579817 0.814269 0.308135 0.881292
0.089985 0.109954 0.16412 0.932147 0.541449 0.440748 0.430723 0.027986 0.428732 0.53596
0.869635 0.353414 0.582253 0.071249 0.43067 0.445438 0.632863 0.277173 0.690245 0.213546
0.806806 0.448468 0.460137 0.251713 0.721387 0.614836 0.389605 0.750749 0.301095 0.822942
0.164091 0.892224 0.46309 0.602414 0.073632 0.577069 0.311047 0.433088 0.95553 0.576564
0.238267 0.358867 0.166104 0.321991 0.440911 0.379365 0.350386 0.831003 0.777742 0.301062
0.099436 0.723328 0.603492 0.103534 0.890042 0.033067 0.015669 0.256781 0.591568 0.997424
0.743889 0.975307 0.475655 0.724345 0.820445 0.63577 0.637703 0.210467 0.21688 0.544641
0.257039 0.206771 0.955119 0.648482 0.42313 0.304216 0.004278 0.07788 0.108215 0.86183
0.19241 0.248724 0.273157 0.568767 0.339769 0.209321 0.758986 0.854213 0.572448 0.493525
0.370675 0.363502 0.052989 0.651691 0.720487 0.181489 0.729522 0.813053 0.387934 0.285297
0.50972 0.531243 0.231967 0.633119 0.272242 0.356871 0.479515 0.564491 0.731814 0.436819
0.531165 0.144926 0.533961 0.362365 0.182073 0.692403 0.76874 0.797186 0.820288 0.322334
0.57374 0.648845 0.315545 0.493628 0.957489 0.682699 0.018719 0.818211 0.81054 0.681996
0.543586 0.281875 0.464107 0.169835 0.19906 0.52485 0.994908 0.200527 0.310928 0.503307
0.795633 0.858614 0.65829 0.417679 0.522723 0.187043 0.681841 0.173055 0.810918 0.841901
0.836581 0.2086 0.49256 0.641788 0.15078 0.755902 0.047176 0.936819 0.358447 0.530004
0.766711 0.65465 0.544771 0.107883 0.296548 0.921418 0.494918 0.454574 0.316163 0.783404
0.030166 0.815846 0.92289 0.140075 0.793361 0.888794 0.527177 0.715692 0.026969 0.662283
0.782376 0.433349 0.046047 0.471159 0.920516 0.945414 0.688757 0.080583 0.052391 0.944164
0.482072 0.590157 0.59521 0.62648 0.384784 0.384483 0.723561 0.19063 0.287968 0.727512
0.122209 0.707452 0.396592 0.508125 0.97117 0.826079 0.401616 0.661694 0.382278 0.807194
0.164428 0.377918 0.297111 0.64579 0.102944 0.306434 0.293639 0.643514 0.929605 0.957645
0.831207 0.752471 0.508409 0.806998 0.246529 0.307219 0.898496 0.209187 0.138377 0.443392
0.967796 0.930627 0.157364 0.151285 0.641029 0.355102 0.554664 0.958128 0.771884 0.303181
0.126512 0.163143 0.668278 0.307189 0.184193 0.687486 0.941034 0.016607 0.743019 0.370864
0.637113 0.864481 0.55347 0.395558 0.723016 0.24485 0.559539 0.748478 0.903323 0.787279
0.593781 0.125018 0.397928 0.423217 0.337637 0.01193 0.160354 0.847261 0.881547 0.327661
0.163702 0.335983 0.393111 0.103055 0.298934 0.250373 0.430724 0.968281 0.174737 0.080402
0.533392 0.359642 0.731249 0.964605 0.665766 0.454268 0.472295 0.769137 0.767292 0.202708
0.708683 0.776425 0.952476 0.684216 0.179214 0.608584 0.330075 0.280119 0.643672 0.16669
0.689752 0.17564 0.527739 0.299214 0.056454 0.994437 0.165859 0.892618 0.426387 0.237804
0.854123 0.451194 0.84043 0.701336 0.146926 0.275853 0.344585 0.978629 0.370638 0.542107
0.250651 0.830126 0.508852 0.968647 0.265893 0.106729 0.556423 0.645297 0.574232 0.375357
0.977903 0.139158 0.07347 0.963622 0.044018 0.283764 0.510736 0.529313 0.814626 0.677299
0.864175 0.387366 0.921463 0.407755 0.104333 0.713586 0.148012 0.062693 0.686503 0.551268
0.315072 0.98352 0.752328 0.487491 0.540621 0.217305 0.081921 0.446164 0.18009 0.362908
0.494083 0.955259 0.252262 0.083756 0.275091 0.11244 0.050938 0.477523 0.062899 0.218305
0.351705 0.574762 0.219315 0.781134 0.417258 0.341208 0.738764 0.223385 0.332721 0.75805
0.671537 0.901648 0.934601 0.844333 0.961514 0.173815 0.039781 0.17507 0.357422 0.593777
0.698868 0.982303 0.243343 0.471303 0.898878 0.22006 0.983244 0.94112 0.720203 0.194308
0.398517 0.056673 0.171272 0.690002 0.05672 0.260529 0.426102 0.617796 0.135771 0.619855
0.261517 0.667458 0.32102 0.447514 0.490624 0.806307 0.564626 0.989565 0.840986 0.915969
0.732167 0.8698 0.758959 0.700127 0.944897 0.569886 0.705171 0.890339 0.564274 0.67967
0.810296 0.962371 0.628768 0.39366 0.364599 0.075272 0.280224 0.477081 0.933484 0.305836
0.276514 0.161654 0.285087 0.413142 0.715213 0.890316 0.04089 0.250263 0.216537 0.496149
0.699828 0.288266 0.561529 0.213015 0.47815 0.25772 0.374039 0.697391 0.64589 0.286577
0.537876 0.493392 0.534004 0.847248 0.420608 0.461938 0.687786 0.747479 0.899557 0.849619
0.208543 0.391944 0.591156 0.995973 0.15847 0.542281 0.580631 0.907125 0.331124 0.442192
0.104947 0.614596 0.134131 0.175381 0.267237 0.882597 0.706696 0.729831 0.920213 0.622809
0.280791 0.423657 0.930981 0.24082 0.115304 0.33998 0.244842 0.947775 0.549023 0.366095
0.351764 0.663053 7.202052 střední hodnota 6.040254
0.122268 0.173667 5.599619 odchylka výběru 0.997234 jaké můžou padat hodnoty
0.53932 0.807578 4.980817 odchylka průměru 0.099723 jaký může padat průměr
0.300796 0.870178 5.082064
0.924633 0.28418 5.558755
0.624549 0.381497 6.074217
0.816754 0.503386 5.308592
0.143611 0.269044 4.183849
0.118194 0.397496 4.970155
0.159803 0.315396 5.167572
0.665229 0.532366 6.69622
0.616193 0.224299 6.238727
0.620686 0.293591 6.132367
0.242423 0.403622 6.354886
0.831355 0.215806 4.563241
0.712384 0.257411 5.140501
0.242987 0.299542 6.555306
0.947642 0.350497 6.688986
0.320698 0.076006 5.549935
0.397704 0.853031 6.494985
0.409627 0.548239 6.557709
0.322914 0.379036 5.95544
0.328461 0.920374 6.880422
0.819433 0.353671 6.94641
0.406078 0.707361 5.92274
0.025719 0.368551 4.16198
0.580253 0.525137 4.722028
0.922754 0.419091 6.089101
0.594383 0.894595 7.775958
0.206569 0.168441 6.954336
0.909655 0.861881 6.207865
0.454456 0.034151 5.846503
0.855276 0.205476 6.416837
0.519863 0.741765 5.840733
0.934568 0.439412 5.431388
0.108379 0.630474 4.804091
0.314396 0.147356 3.573127
0.615667 0.412244 5.962872
0.848928 0.882002 8.775399
0.17315 0.574109 4.64506
0.480137 0.454882 7.136551
0.858787 0.357661 6.370425
0.792461 0.245934 5.55064
0.715782 0.274416 5.635665
0.366518 0.514291 6.013138
0.874187 0.427735 7.179748
0.272802 0.894351 7.207165
0.478048 0.036188 7.748534
0.138566 0.907417 5.234099
0.916433 0.458911 7.66027
0.435993 0.116323 4.25412
0.807472 0.636479 6.010437
0.645137 0.914719 7.127595
0.749286 0.187691 5.985726
0.935255 0.303827 5.40478
0.512616 0.703877 5.530834
0.499882 0.779839 7.264823
0.949818 0.438085 5.234863
0.744067 0.663585 5.918972
0.600927 0.788568 5.946133
0.286907 0.683923 5.718631
0.800037 0.163891 6.119369
0.728598 0.096064 6.826074
0.839078 0.545834 5.577896
0.959438 0.692076 7.59921
0.954292 0.503754 6.416701
0.798907 0.983621 7.123568
0.860483 0.557697 6.941434
0.612276 0.183619 6.160652
0.852062 0.406047 6.250966
0.698247 0.879333 7.361989
0.560697 0.238327 5.518053
0.18757 0.023822 5.353677
0.263657 0.520748 6.575463
0.020787 0.096469 4.325581
0.285458 0.85457 7.557135
0.998052 0.57236 5.676749
0.64119 0.613446 4.453937
0.39418 0.362423 6.676959
0.709091 0.138806 6.178052
0.784367 0.117261 5.367533
0.697202 0.156817 6.35984
0.685911 0.595944 6.36406
0.190037 0.966018 6.169964
0.925342 0.276054 6.04855
0.850856 0.318666 5.536943
0.060994 0.83161 3.875162
0.542499 0.588418 5.869217
0.32974 0.299005 6.282243
0.576181 0.303303 7.233114
0.323693 0.746042 4.502973
0.104836 0.791812 7.202235
0.865634 0.144573 8.425496
0.782874 0.6348 6.649264
0.579167 0.608845 4.933776
0.590115 0.531179 5.623699
0.722169 0.279112 7.480788
0.177585 0.373105 5.700127
0.209481 0.856167 6.224087
0.269065 0.628589 5.336921
3.679541 třída dolní hranice horní hranice
3.833203 real fikce 1 3.3 3.8
4.012018 počet tříd 10 10 2 3.8 4.3
4.069203 min 3.679541 3.3 3 4.3 4.8
4.152368 max 8.288162 8.3 4 4.8 5.3
4.153726 rozsah 4.60862 5 5 5.3 5.8
4.156057 šířka třídy 0.460862 0.5 6 5.8 6.3
4.171883 7 6.3 6.8
4.312534 8 6.8 7.3
4.322112 9 7.3 7.8
4.405967 10 7.8 8.3
4.496942
4.708576
4.725656
Histogram
4.744835 25
4.752804
4.760323 20
4.786728
4.821443 15
4.832159
4.838942 10
4.840501
4.996104 5
5.104264
5.172568 0
<3,3;3,8 (3,8;4,3> (4,3;4,8> (4,8;5,3> (5,3;5,8> (5,8;6,3> (6,3;6,8> (6,8;7,3> (7,3;7,8>
5.219824 >
5.251562
5.255837
5.301754
5.330608
5.357823
5.41176
5.438671
5.526757
5.537657
5.559102
5.570128
5.582044
5.626799
5.627021
5.655615
5.658397
5.690724
5.710153
5.757357
5.769939
5.778371
5.791802
5.79955
5.838619
5.848294
5.913705
5.953684
5.972699
6.07155
6.075417
6.138666
6.142481
6.164484
6.187935
6.369998
6.386599
6.392114
6.446855
6.486498
6.511254
6.515207
6.52003
6.560568
6.564726
6.590075
6.606952
6.613268
6.629231
6.643438
6.654947
6.699931
6.741805
6.779848
6.815048
6.883679
6.890435
6.916245
6.963118
7.033031
7.109371
7.11706
7.155817
7.156069
7.365194
7.373175
7.455476
7.589699
7.598203
7.612262
7.670049
7.756849
8.159321
8.229306
8.288162
 interval četnost četnosti
<3,3;3,8> 1 1
(3,8;4,3> 7 7 mačkat ctrl+shift+enter označit celý sloupec
(4,3;4,8> 10
(4,8;5,3> 10 zafixování pomocí f4
(5,3;5,8> 21
(5,8;6,3> 11
(6,3;6,8> 19
(6,8;7,3> 10
(7,3;7,8> 8
(7,8;8,3> 3

ogram

8> (5,8;6,3> (6,3;6,8> (6,8;7,3> (7,3;7,8> (7,8;8,3>

3.679541 1 0.01 0.018805 střední hodnota 5.9221816
3.833203 2 0.02 0.026395 směrodatná odchylka 1.0786674
4.012018 3 0.03 0.038292
4.069203 4 0.04 0.042913
4.152368 5 0.05 0.050426 medián 5.8434568
4.153726 6 0.06 0.050556 dolní kvartil 5.2080099
4.156057 7 0.07 0.050782 horní kvartil 6.646315
4.171883 8 0.08 0.052332
4.312534 9 0.09 0.067816
4.322112 10 0.10 0.068987 decily
4.405967 11 0.11 0.079916 1. decil 4.3975813
4.496942 12 0.12 0.093201 3. decil 5.3496584
4.708576 13 0.13 0.130274
4.725656 14 0.14 0.133658
4.744835 15 0.15 0.13753 percentil
4.752804 16 0.16 0.139161 27. percentil 5.2546828
4.760323 17 0.17 0.140712
4.786728 18 0.18 0.146252
4.821443 19 0.19 0.153755
4.832159 20 0.20 0.156121
4.838942 21 0.21 0.157632
4.840501 22 0.22 0.15798
4.996104 23 0.23 0.195298
5.104264 24 0.24 0.224146
5.172568 25 0.25 0.243545
5.219824 26 0.26 0.25748

f(x)
5.251562 27 0.27 0.267066
5.255837 28 0.28 0.268371
5.301754 29 0.29 0.282585
5.330608 30 0.30 0.291698
5.357823 31 0.31 0.300418
0.0999999999
5.41176 32 0.32 0.318036 0.0499999999
5.438671 33 0.33 0.326987 -2.567390744445
5.526757 34 0.34 0.356964 -0.0500000000

5.537657 35 0.35 0.36074

5.559102 36 0.36 0.368209
5.570128 37 0.37 0.372069
5.582044 38 0.38 0.376255
5.626799 39 0.39 0.392104
5.627021 40 0.40 0.392183
5.655615 41 0.41 0.402405
5.658397 42 0.42 0.403404
5.690724 43 0.43 0.415049
5.710153 44 0.44 0.422084
5.757357 45 0.45 0.439276
5.769939 46 0.46 0.44388
5.778371 47 0.47 0.446969
5.791802 48 0.48 0.451897
5.79955 49 0.49 0.454743
5.838619 50 0.50 0.469126
5.848294 51 0.51 0.472694
5.913705 52 0.52 0.496865
5.953684 53 0.53 0.51165
5.972699 54 0.54 0.518677
6.07155 55 0.55 0.555067
6.075417 56 0.56 0.556484
6.138666 57 0.57 0.579532
6.142481 58 0.58 0.580914
6.164484 59 0.59 0.588867
6.187935 60 0.60 0.597303
6.369998 61 0.61 0.660987
6.386599 62 0.62 0.666601
6.392114 63 0.63 0.668458
6.446855 64 0.64 0.686661
6.486498 65 0.65 0.699569
6.511254 66 0.66 0.707505
6.515207 67 0.67 0.708764
6.52003 68 0.68 0.710295
6.560568 69 0.69 0.723017
6.564726 70 0.70 0.724307
6.590075 71 0.71 0.732102
6.606952 72 0.72 0.73723
6.613268 73 0.73 0.739136
6.629231 74 0.74 0.743922
6.643438 75 0.75 0.748142
6.654947 76 0.76 0.751534
6.699931 77 0.77 0.764554
6.741805 78 0.78 0.776327
6.779848 79 0.79 0.786727
6.815048 80 0.80 0.796094
6.883679 81 0.81 0.813636
6.890435 82 0.82 0.815311
6.916245 83 0.83 0.821623
6.963118 84 0.84 0.832733
7.033031 85 0.85 0.848456
7.109371 86 0.86 0.864466
7.11706 87 0.87 0.866012
7.155817 88 0.88 0.873619
7.156069 89 0.89 0.873667
7.365194 90 0.90 0.909515
7.373175 91 0.91 0.910715
7.455476 92 0.92 0.92241
7.589699 93 0.93 0.938936
7.598203 94 0.94 0.939883
7.612262 95 0.95 0.941422
7.670049 96 0.96 0.947426
7.756849 97 0.97 0.955516
8.159321 98 0.98 0.98096
8.229306 99 0.99 0.983777
8.288162 100 1.00 0.985862
 1. způsob - sloupec C
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1

2. způsob - sloupec D
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
f(x)

0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.0999999999999998
0.0499999999999998
-2.56739074444567E-16
-0.05000000000000033.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4

m [g]
20546.1369 124.6298 (20550+-130)
(2055+-13)*10 díky tomu víme že ručíme pouze za desítky a ne za jednotky v 0
y a ne za jednotky v 0