4. Prosek i medijana niza brojeva¶

U ovoj lekciji ćeš naučiti:

kako da izračunaš prosek niza brojeva;
kako da sortiraš niz i nađeš njegovu medijanu;
kako da filtriraš podatke; i
kako da na istom grafikonu prikažeš i podatke i njihov prosek, ili podatke i njihovu medijanu.

4.1. Prosek niza¶

Postoji mnogo situacija kada se niz brojeva može zgodno opisati nekom karakterističnom vrednošću. Na primer, učenici dobijaju ocene iz mnogo predmeta, ali na kraju školske godine školski sistem želi da "izvede" jednu ocenu i da tom ocenom okarakteriše rad učenika u toj godini.

Vremenom se kao jedan od pogodnih predstavnika niza brojeva pokazao prosek. Prosek niza brojeva se računa ovako:

$$ \hbox{prosek niza } [x_1, x_2, \dots, x_n] = \frac{x_1 + x_2 + \dots + x_n}{n}. $$

Dakle, da bismo dobili prosek niza brojeva saberemo sve elemente niza i tako dobijeni broj podelimo dužinom niza.

U Pajtonu se obe ove aktivnosti mogu obaviti pozivom odgovarajuće ugrađene funkcije: funkcija len računa dužinu niza, dok funkcija sum računa zbir elemenata niza brojeva.

Na primer:

L = [1, 3, 5, 7, 9, 10]
print(len(L))
print(sum(L))

6
35

(Primeti da su ove funkcije ugrađene u Pajton i da nema potrebe loviti ih po bibliotekama!)

Prema tome, prosek niza brojeva se u Pajtonu računa ovako:

print("Prosek niza brojeva", L, "je", sum(L) / len(L))

Prosek niza brojeva [1, 3, 5, 7, 9, 10] je 5.833333333333333

Kako ćemo u mnogo navrata računati prosek, definisaćemo novu funkciju koja ga računa. U prethodnim razredima smo se već sreli sa definicijama novih funkcija u Pajtonu i zato mali program koji sledi ne bi trebalo da predstavlja iznenađenje za tebe:

def prosek(L):
    return sum(L) / len(L)

Prethodni program je u sistem uneo novu definiciju: funkcija prosek će prihvatiti neki niz L i onda će kao rezultat svog rada vratiti zbir elemenata niza L podeljen dužinom niza L (dakle, prosek elemenata tog niza).

Primeti da je spisak Pajton naredbi koje predstavljaju telo funkcije i objašnjavaju šta funkcija radi uvučen za četiri praznine.

Da vidimo kako radi naša nova funkcija:

print("Prosek niza brojeva", L, "je", prosek(L))

Prosek niza brojeva [1, 3, 5, 7, 9, 10] je 5.833333333333333

U ćeliji ispod unete su ocene jednog učenika iz informatike i prikazan je njihov prosek:

ocene = [5, 3, 5, 4, 4, 5]
print("Prosek ocena iz informatike je", prosek(ocene))

Prosek ocena iz informatike je 4.333333333333333

Ako ćemo iskreno, prosek ocena se uvek prikazuje zaokružen na dve decimale. U Pajtonu postoji ugrađena funkcija round(x, n) koja zaokružuje dati broj x na n decimala. Na primer:

round(1.666666666, 2)

1.67

Prema tome, prosek ocena iz informatike sada možemo da dobijemo ovako:

print("Prosek ocena iz informatike je", round(prosek(ocene), 2))

Prosek ocena iz informatike je 4.33

4.2. Sortiranje niza i medijana¶

Sortirati niz znači ispremeštati njegove elemente tako da budu poređani po veličini, od manjih ka većim ili obrnuto. Na primer:

$$ [3, 1, 2, 5, 0, -1, 4] \to [-1, 0, 1, 2, 3, 4, 5] $$

Ugrađena funkcija sort sortira niz i poziva se ovako:

L = [3, 1, 2, 5, 0, -1, 4]
L.sort()

Ako proverimo vrednost promenljive L nakon poziva funkcije sort videćemo da su elementi liste sada poređani od manjih ka većim vrednostima:

L

[-1, 0, 1, 2, 3, 4, 5]

Ako želimo da poređamo elemente liste L od većih ka manjim vrednostima, to možemo da uradimo ovako:

L.sort(reverse=True)
L

[5, 4, 3, 2, 1, 0, -1]

Opcija reverse=True kaže funkciji sort da želimo da sortiramo elemente liste u "obrnutom" poretku: od većih ka manjim vrednostima.

Ako su podaci sa kojima radimo "jako razbacani" i "imaju velika odstupanja" može se desiti da prosek niza nije dobar predstavnik celog niza. Zato se kao druga karakteristična vrednost niza često koristi medijana.

Medijana niza je element na sredini sortiranog niza.

def medijana(L):
    n = len(L)
    L.sort()
    return L[n//2]

U mnogim situacijama medijana bolje predstavlja „srednju vrednost“ niza nego aritmetička sredina niza. Evo primera.

U listi zarade date su mesečne zarade zaposlenih u jednoj kompaniji iskazane u američkim dolarima.

zarade = [647, 570, 587, 576, 646, 519, 585, 686, 644, 604, 562, 589, 536, 675, 514, 620, 561, 567, 673, 577, 627, 643, 592, 509, 645, 625, 645, 608, 502, 552, 647, 601, 632, 583, 523, 546, 681, 637, 636, 541, 587, 573, 530, 596, 695, 619, 619, 543, 573, 672, 557, 668, 653, 513, 631, 656, 567, 538, 519, 576, 547, 687, 597, 644, 676, 661, 622, 593, 591, 629, 526, 536, 508, 510, 514, 584, 549, 632, 527, 602, 633, 636, 637, 639, 532, 619, 578, 534, 513, 540, 638, 580, 642, 553, 530, 699, 642, 556, 629, 620, 685, 574, 656, 673, 516, 591, 628, 513, 594, 667, 513, 528, 694, 660, 632, 570, 671, 522, 655, 694, 684, 635, 559, 561, 541, 643, 516, 655, 522, 554, 611, 669, 564, 540, 642, 645, 590, 658, 669, 530, 679, 572, 700, 637, 650, 577, 696, 695, 551, 586, 581, 547, 545, 558, 670, 548, 536, 622, 586, 700, 585, 568, 582, 589, 649, 575, 584, 514, 526, 686, 668, 532, 582, 651, 693, 693, 556, 509, 562, 672, 673, 658, 573, 509, 698, 652, 541, 605, 659, 688, 591, 691, 548, 699, 656, 642, 598, 562, 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619, 647, 628, 687, 638, 672, 554, 635, 526, 536, 576, 502, 560, 592, 638, 587, 518, 570, 640, 519, 510, 682, 647, 666, 549, 515, 651, 656, 569, 691, 593, 550, 522, 683, 574, 597, 628, 503, 672, 544, 516, 655, 665, 665, 616, 631, 557, 565, 607, 684, 655, 622, 586, 628, 629, 645, 602, 570, 626, 552, 697, 534, 570, 672, 506, 538, 626, 595, 582, 570, 695, 600, 689, 535, 555, 619, 502, 589, 589, 673, 643, 618, 684, 527, 510, 579, 500, 547, 561, 664, 647, 637, 531, 611, 585, 582, 519, 549, 689, 696, 516, 536, 591, 542, 697, 631, 641, 667, 509, 635, 643, 555, 667, 592, 633, 650, 619, 628, 562, 576, 602, 555, 637, 547, 605, 597, 563, 562, 620, 628, 652, 536, 618, 695, 517, 654, 588, 598, 598, 633, 692, 521, 641, 564, 610, 693, 507, 594, 563, 528, 532, 669, 597, 648, 608, 577, 677, 625, 657, 668, 554, 517, 508, 568, 629, 660, 519, 597, 668, 591, 655, 639, 646, 562, 664, 551, 635, 526, 581, 637, 503, 500, 531, 533, 700, 570, 643, 609, 633, 587, 697, 650, 603, 536, 661, 672, 652, 588, 687, 585, 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508, 677, 645, 650, 569, 521, 685, 657, 523, 576, 591, 518, 558, 522, 667, 520, 544, 696, 682, 688, 635, 530, 667, 646, 606, 507, 510, 674, 618, 648, 650, 637, 588, 535, 683, 601, 511, 586, 533, 628, 542, 660, 604, 509, 635, 555, 667, 509, 551, 582, 679, 679, 680, 680, 513, 657, 685, 558, 545, 555, 608, 571, 610, 650, 587, 597, 678, 526, 544, 622, 661, 622, 612, 548, 535, 550, 564, 571, 515, 611, 651, 664, 682, 588, 676, 665, 563, 646, 614, 511, 571, 698, 527, 518, 504, 611, 657, 626, 606, 577, 589, 621, 514, 549, 536, 673, 608, 558, 624, 569, 685, 517, 604, 555, 540, 521, 571, 584, 619, 509, 662, 680, 681, 692, 522, 621, 629, 679, 590, 699, 586, 595, 555, 615, 520, 532, 554, 610, 659, 646, 660, 656, 599, 568, 603, 586, 580, 547, 659, 519, 532, 511, 560, 609, 688, 620, 534, 656, 523, 561, 610, 560, 615, 569, 535, 515, 516, 568, 649, 566, 562, 509, 519, 588, 637, 609, 527, 617, 534, 582, 632, 687, 525, 691, 544, 559, 571, 545, 537, 658, 675, 545, 557, 685, 618, 531, 524, 566, 578, 635, 650, 598, 511, 594, 592, 619, 509, 552, 562, 516, 667, 507, 575, 648, 529, 503, 563, 544, 624, 627, 654, 645, 668, 650, 509, 560, 571, 609, 505, 661, 606, 681, 584, 599, 624, 627, 572, 538, 622, 502, 522, 669, 680, 513, 569, 520, 635, 629, 519, 548, 640, 614, 601, 611, 680, 699, 539, 699, 517, 679, 519, 595, 509, 638, 509, 641, 583, 512, 610, 561, 589, 684, 534, 600, 600, 551, 543, 542, 673, 694, 592, 585, 584, 613, 531, 592, 685, 589, 550, 699, 552, 598, 546, 682, 603, 694, 681, 655, 699, 699, 655, 627, 618, 500, 542, 607, 680, 698, 562, 558, 647, 576, 635, 529, 541, 639, 604, 511, 506, 598, 642, 625, 588, 669, 655, 646, 560, 524, 586, 605, 676, 617, 527, 652, 683, 652, 554, 601, 664, 571, 608, 602, 519, 511, 554, 539, 664, 523, 627, 592, 618, 555, 642, 667, 558, 511, 595, 529, 568, 516, 660, 642, 500, 694, 655, 613, 539, 656, 515, 589, 515, 546, 615, 614, 697, 674, 633, 692, 557, 635, 565, 509, 569, 606, 642, 697, 503, 562, 500, 565, 572, 627, 502, 671, 624, 587, 662, 561, 504, 618, 531, 680, 660, 567, 645, 611, 618, 527, 617, 688, 513, 692, 612, 682, 517, 690, 583, 626, 580, 608, 513, 577, 658, 634, 644, 588, 692, 634, 538, 611, 554, 538, 600, 602, 699, 538, 631, 542, 564, 568, 591, 664, 528, 591, 693, 679, 649, 533, 694, 562, 668, 574, 652, 669, 700, 508, 680, 600, 568, 509, 685, 583, 514, 536, 525, 624, 671, 539, 665, 700, 700, 533, 697, 560, 665, 648, 538, 509, 690, 695, 681, 615, 646, 587, 538, 612, 611, 697, 652, 688, 645, 668, 650, 503, 628, 563, 517, 568, 652, 518, 592, 559, 688, 594, 549, 678, 565, 571, 575, 691, 641, 568, 644, 689, 625, 616, 632, 694, 612, 639, 671, 621, 665, 502, 505, 596, 547, 591, 588, 553, 508, 581, 514, 534, 533, 526, 667, 548, 541, 566, 511, 520, 682, 645, 634, 624, 693, 630, 674, 544, 700, 544, 577, 656, 548, 636, 680, 641, 504, 554, 587, 683, 541, 542, 639, 505, 607, 517, 656, 529, 572, 584, 606, 690, 624, 589, 516, 675, 542, 656, 660, 697, 668, 628, 523, 597, 554, 615, 681, 534, 602, 583, 689, 636, 633, 550, 583, 612, 647, 658, 627, 597, 553, 647, 588, 648, 580, 548, 594, 536, 513, 700, 651, 573, 691, 681, 550, 683, 572, 619, 590, 509, 633, 562, 694, 694, 679, 537, 542, 637, 510, 566, 533, 596, 619, 688, 529, 673, 545, 551, 550, 548, 629, 511, 561, 538, 513, 599, 549, 561, 517, 632, 541, 637, 636, 604, 563, 618, 630, 659, 640, 622, 666, 661, 626, 524, 698, 589, 655, 621, 554, 603, 683, 526, 684, 678, 589, 640, 553, 608, 698, 550, 637, 604, 521, 526, 661, 649, 606, 577, 549, 688, 626, 668, 672, 619, 664, 608, 505, 609, 519, 680, 592, 681, 597, 502, 534, 662, 551, 619, 525, 591, 512, 634, 677, 656, 694, 642, 651, 681, 694, 668, 643, 549, 619, 600, 624, 545, 582, 890234, 672, 699, 549, 571, 688, 542, 691, 533, 670, 603, 583, 670, 550, 544, 500, 596, 700, 551, 535, 639, 634, 630, 592, 647, 518, 692, 566, 581, 645, 573, 685, 623, 533, 549, 535, 675, 637, 504, 500, 629, 508, 501, 654, 566, 675, 535, 640, 552, 510, 676, 597, 641, 567, 547, 517, 506, 563, 577, 542, 588, 575, 590, 625, 649, 564, 514, 517, 666, 591, 569, 690, 534, 672, 642, 505, 619, 566, 637, 570, 521, 582, 546, 626, 539, 501, 512, 636, 533, 545, 532, 608, 658, 589, 626, 608, 520, 688, 663, 615, 521, 571, 551, 520, 510, 531, 654, 659, 644, 588, 565, 651, 647, 630, 628, 642, 679, 539, 645, 616, 628, 639, 532, 576, 563, 597, 586, 683, 580, 594, 631, 656, 678, 661, 606, 595, 624, 649, 640, 624, 700, 618, 502, 590, 671, 515, 561, 647, 698, 682, 687, 513, 593, 655, 548, 668, 687, 532, 653, 529, 601, 674, 698, 555, 650, 515, 614, 518, 569, 531, 612, 564, 503, 647, 500, 635, 696, 611, 610, 586, 670, 588, 607, 649, 664, 594, 517, 685, 540, 502, 533, 585, 654, 700, 519, 627, 586, 674, 616, 614, 625, 634, 658, 574, 667, 593, 582, 547, 604, 645, 552, 574, 633, 605, 640, 629, 662, 661, 676, 512, 613, 537, 570, 548, 568, 605, 622, 670, 693, 647, 660, 500, 644, 614, 551, 642, 660, 637, 652, 573, 560, 672, 613, 645, 601, 688, 657, 617, 665, 588, 579, 562, 630, 567, 539, 548, 571, 680, 675, 550, 634, 677, 576, 603, 691, 675, 683, 537, 559, 637, 512, 699, 623, 594, 538, 678, 508, 571, 642, 524, 515, 567, 570, 607, 582, 683, 680, 624, 623, 666, 522, 632, 620, 558, 526, 631, 539, 600, 686, 604, 628, 632, 613, 646, 554, 616, 680, 577, 595, 606, 511, 639, 507, 662, 644, 508, 585, 680, 626, 522, 647, 679, 519, 590, 571, 541, 550, 591, 572, 695, 688, 661, 647, 626, 535, 688, 656, 688, 645, 634, 535, 569, 526, 524, 536, 611, 691, 656, 542, 520, 665, 679, 589, 509, 641, 542, 569, 621, 583, 559, 590, 649, 683, 599, 520, 684, 629, 519, 539, 506, 511, 615, 689, 625, 635, 680, 547, 557, 561, 644, 512, 624, 648, 656, 651, 659, 582, 676, 685, 576, 576, 656, 694, 675, 683, 547, 645, 645, 558, 660, 639, 592, 682, 693, 591, 663, 645, 688, 677, 569, 587, 614, 561, 638, 598, 521, 545, 620, 671, 523, 534, 553, 573, 618, 680, 529, 670, 513, 559, 659, 596, 545, 552, 651, 589, 636, 627, 525, 588, 662, 685, 577, 655, 605, 503, 585, 622, 569, 511, 629, 584, 682, 651, 663, 514, 518, 540, 584, 550, 681, 588, 607, 586, 540, 688, 541, 651, 611, 546, 525, 632, 652, 657, 567, 574, 505, 506, 632, 609, 663, 522, 675, 579, 682, 700, 680, 566, 647, 524, 554, 610, 602, 633, 513, 606, 565, 654, 684, 509, 629, 694, 595, 650, 506, 501, 667, 688, 590, 602, 587, 554, 621, 552, 581, 621, 563, 562, 687, 672, 605, 636, 633, 545, 532, 654, 620, 561, 605, 574, 628, 556, 674, 689, 545, 617, 559, 513, 693, 587, 519, 582, 635, 586, 611, 599, 564, 691, 595, 508, 694, 599, 576, 513, 597, 520, 504, 521, 664, 533, 546, 679, 504, 563, 522, 700, 522, 588, 597, 572, 595, 644, 572, 504, 582, 556, 615, 658, 640, 657, 667, 509, 698, 539, 596, 589, 639, 559, 564, 629, 680, 694, 670, 688, 620, 506, 682, 530, 557, 640, 594, 528, 585, 648, 524, 517, 555, 567, 510, 603, 507, 529, 519, 504, 580, 599, 696, 534, 649, 665, 538, 639, 521, 527, 588, 521, 583, 641, 597, 606, 655, 528, 633, 697, 614, 668, 549, 502, 506, 640, 606, 672, 516, 627, 594, 507, 615, 571, 509, 648, 530, 594, 664, 567, 659, 543, 570, 653, 559, 534, 646, 606, 524, 562, 565, 595, 633, 597, 641, 603, 638, 589, 616, 592, 645, 592, 641, 638, 587, 665, 536, 516, 509, 632, 594, 675, 547, 500, 586, 558, 693, 566, 699, 661, 688, 664, 603, 576, 657, 669, 662, 601, 655, 557, 656, 539, 593, 596, 506, 524, 695, 612, 504, 626, 603, 616, 681, 548, 501, 522, 569, 655, 631, 621, 691, 596, 540, 531, 558, 565, 683, 611, 564, 614, 513, 621, 520, 559, 689, 530, 596, 620, 666, 645, 697, 634, 693, 699, 676, 566, 700, 643, 581, 605, 517, 556, 685, 677, 533, 515, 532, 682, 588, 661, 667, 674, 562, 601, 621, 551, 509, 699, 531, 540, 500, 694, 605, 603, 509, 676, 672, 680, 649, 649, 584, 511, 502, 692, 618, 597, 684, 613, 503, 654, 536, 635, 651, 608, 579, 560, 560, 597, 520, 538, 677, 660, 651, 636, 598, 635, 506, 623, 504, 646, 513, 560, 584, 582, 691, 613, 646, 524, 642, 648, 590, 512, 597, 591, 540, 692, 631, 583, 690, 512, 633, 682, 535, 572, 676, 504, 574, 507, 539, 570, 630, 699, 578, 648, 554, 580, 507, 645, 531, 592, 623, 523, 647, 656, 685, 524, 644, 591, 548, 528, 555, 539, 646, 635, 649, 663, 643, 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523, 661, 579, 664, 670, 579, 505, 673, 631, 695, 577, 653, 514, 556, 651, 530, 664, 559, 630, 699, 506, 696, 653, 674, 636, 618]

U ovoj listi ima preko 10.000 podataka:

len(zarade)

10012

Prosečna zarada u kompaniji je:

prosek(zarade)

3911.713044346784

Međutim, medijana ovog niza je:

medijana(zarade)

600

Dakle, prosečna zarada u kompaniji je oko 3912 američkih dolara, ali medijana svih zarada je 600 američkih dolara. To znači da polovina zaposlenih u toj kompaniji ima zaradu koja iznosi 600 američkih dolara ili manje. Kako je to moguće?

Da bismo shvatili šta se desilo, moramo da izvršimo detaljniju analizu.

4.3. Filtriranje podataka¶

Filtrirati podatke znači iz datog niza podataka izdvojiti one koji su nam na neki način interesantni.

Da bismo shvatili kako je moguće da je u prethodnom primeru prosečna zarada šest puta veća od medijalne, filtriraćemo natprosečne zarade. Filtriranje liste u Pajtonu se može postići konstrukcijom koja izgleda ovako:

[x for x in Lista if Uslov(x)]

Ova konstrukcija u novu listu pokupi sve elemente x liste Lista koji ispunjavaju Uslov. To je kao kad u matematici napišemo:

$$ \{x \mid x \in \mathrm{Lista} \land \mathrm{Uslov}(x) \} $$

Nama su u prethodnom primeru interesantne zarade koje su iznad proseka. Da bismo videli koliko ih ima i koje su to zarade prvo ćemo prosečnu zaradu smestiti u promenljivu i onda ćemo filtrirati listu zarade:

prosecna_zarada = prosek(zarade)
natprosecne_zarade = [x for x in zarade if x >= prosecna_zarada]

Natprosečne zarade su:

natprosecne_zarade

[890234,
 950611,
 1211345,
 1211900,
 2341809,
 2458351,
 3211459,
 3411800,
 3811325,
 4215311,
 4231800,
 5211765]

i vidimo da ih ima svega

len(natprosecne_zarade)

12

Dakle, u ovoj kompaniji 12 zaposlenih ima ogromne zarade, a 10.000 zaposlenih ima zarade koje su ispod proseka. Ovih dvanaest nesrazmerno visokih zarada povećava prosek i daje utisak da "prosečna zarada u ovoj kokmpaniji i nije toliko loša", iako je stvarno stanje znatno lošije.

Situacije u kojima se medijana jako razlikuje od proseka nam govore da su podaci izuzetno neravnomerni i da je potrebno uložiti dodatni napor da bi se shvatilo kakvo stanje oni opisuju.

4.4. Prikazivanje podataka, njihovog proseka i njihove medijane¶

Jedan način da vidimo odnos proseka i medijane i kako oni predstavljaju podatke je da situaciju vizuelizujemo.

Krenimo od jednog jednostavnog primera. Pretpostavimo da je na polugodištu jedan učenik imao sledeće ocene iz navedenih predmeta:

Predmet	Ocena
Matematika	2
Srpski	4
Likovno	5
Istorija	3
Fizičko	5
Muzičko	4
Tehničko	5

Podatke možemo predstaviti pomoću dve liste, ovako:

predmeti = ["mat", "srp", "lik", "ist", "fiz", "muz", "tio"]
ocene    = [2,     4,     5,     3,     5,     4,     5    ]

Želimo da prikažemo njegove ocene histogramom i da prosečna ocena bude označena crvenom linijom kako bismo mogli da vidimo koje ocene su iznad proseka, a koje ispod.

Prvo ćemo učitati biblioteku za crtanje grafikona:

import matplotlib.pyplot as plt

Histogram sa ocenama možemo da nacrtamo veoma jednostavno:

plt.figure(figsize=(10,5))
plt.bar(predmeti, ocene)
plt.title("Ocene na polugodistu")
plt.show()
plt.close()

Sada želimo da preko histograma nacrtamo crvenu liniju koja predstavlja prosečnu ocenu. Prvo ćemo izračunati prosečnu ocenu po:

po = prosek(ocene)

a onda ćemo na gornji dijagram dodati i niz podataka koji izgleda ovako:

[po, po, po, po, po, po, po]

plt.figure(figsize=(10,5))
plt.bar(predmeti, ocene)
plt.plot(predmeti, [po, po, po, po, po, po, po], color="r")
plt.title("Ocene na polugodistu")
plt.show()
plt.close()

Ako jedan isti podatak s treba ponoviti n puta možemo da pišemo kao gore:

[s, s, s, (i tako dalje)]

ali možemo da to zapišemo kraće ovako:

[s]*n

Oznakom [s]*n smo Pajtonu rekli da želimo da napravimo novi niz koji se dobija tako što se niz [s] "umnoži" n puta. Na primer, [5]*7 = [5, 5, 5, 5, 5, 5, 5]. (Takođe je [6, 7, 8]*3 = [6, 7, 8, 6, 7, 8, 6, 7, 8], ali nam ovo za sada neće biti potrebno.)

Tako dobijamo sledeću verziju programa:

plt.figure(figsize=(10,5))
plt.bar(predmeti, ocene)
plt.plot(predmeti, [po] * len(ocene), color="r")
plt.title("Ocene na polugodistu")
plt.show()
plt.close()

Za kraj ćemo dijagramu dodati legendu:

plt.figure(figsize=(10,5))
plt.bar(predmeti, ocene, label="ocene")
plt.plot(predmeti, [po] * len(ocene), color="r", label="prosek")
plt.title("Ocene na polugodistu")
plt.legend()
plt.show()
plt.close()

Sada ćemo da vizuelizujemo zarade u kompaniji o kojoj smo govorili u prethodnim odeljcima. (Lista sa kojom radimo je veoma velika, tako da ovo može potrajati! Samo hrabro o strpljivo!)

n = len(zarade)
plt.bar(range(n), zarade)
plt.show()
plt.close()

Dakle, ništa se ne vidi.

Moraćemo da povećamo dijagram i da pribegnemo još jednom lukavstvu. Pošto mi već znamo da je prosečna zarada oko 3912 američkih dolara i da ima samo 12 zaposlenih u toj kompaniji koji primaju toliko ili više, ograničićemo vrednosti koje se prikazuju na $y$-osi. Odmah ćemo prikazati i prosek crvenom linijom.

n = len(zarade)
plt.figure(figsize=(15,5))
plt.bar(range(n), zarade, color="b")
plt.plot([0, n-1], [prosecna_zarada, prosecna_zarada], color="r")
plt.ylim(0,6000)
plt.show()
plt.close()

Na ovom dijagramu se jasno vidi kako su nesrazmerno velike zarade nekolicine zaposlenih "povukle prosek za sobom".

Pogledajmo sada gde je medijana. Nju ćemo predstaviti kao dijagram sa samo jednim crvenim stubićem na sredini niza.

n = len(zarade)
plt.figure(figsize=(15,5))
plt.bar(range(n), zarade, color="b")
plt.bar([n//2], [zarade[n//2]], color="r")
plt.ylim(0,6000)
plt.show()
plt.close()

Gde je crvena crtica?

Pošto na relativno malom prostoru prikazujemo preko 10.000 podataka pojedinačni stubići su jako uski i stubić koji predstavlja medijana se ne vidi. Da bismo je istakli promenićemo širinu stubića opcijom width.

n = len(zarade)
plt.figure(figsize=(15,5))
plt.bar(range(n), zarade, color="b")
plt.bar([n//2], [zarade[n//2]], color="r", width=100)
plt.ylim(0,6000)
plt.show()
plt.close()

4.5. Zadaci¶

Zadatke uradi u Džupajteru.

Zadatak 1. Jedna zbirka kratkih priča za decu ima 12 strana - po jedna priča na svakoj strani. Priče imaju mali broj reči, i to, po stranama: 271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 i 314. Koliki je prosečan broj reči po priči u ovoj knjizi?

Zadatak 2.

(a) Mirko iz muzičkog ima 5, 4, 5 i još jednu ocenu koja se ne vidi jer se preko nje razlilo mastilo. Prosek njegovih ocena iz muzičkog je 4. Koja je to ocena preko koje se razlilo mastilo?

(b) Koliko još petica Mirko treba da dobije da bi nastavnica muzičkog za kraj godine morala da mu zaključi ocenu 5? (Prema Pravilniku o ocenjivanju u osnovnim školama, ako je prosek ocena upisanih u dnevnik 4,50 ili više, nastavnik mora da zaključi ocenu 5.)

(Pomoć: rešenje zadatka pod (a) izračunaj - za to ti ne treba Pajton; rešenje zadatka pod (b) možeš da izračunaš, ali možeš i da ga pogodiš tako što ćeš eksperimentisati sa raznim mogućnostima Mirkovih ocena iz muzičkog - koristi funkcije prosek i round.)

Zadatak 3. Petar u dnevniku ima nekoliko ocena iz informatike, svakako manje od 10. Znamo da su 25% njegovih ocena iz informatike petice, a 12,5% njegovih ocena su trojke.

(a) Koliko ocena iz informatike ima Petar u dnevniku?

(b) Koliko Petar ima petica, a koliko trojki iz informatike?

(v) Koliki je prosek njegovih ocena iz informatike, ako znamo da nema nijednu jedinicu i nijednu dvojku?

Zadatak 4. Vesnine ocene iz informatike su date u sledećem nizu:

vesna_ocene = [5, 5, 4, 5, 4, 3, 4, 5, 5, 5]

Neka je po promenljiva u koju smo smestili prosek Vesninih ocena:

po = prosek(vesna_ocene)

Pogledaj pažljivo sledeću ćeliju, pa odgovori na pitanja nakon nje:

plt.figure(figsize=(15,7))
plt.bar(range(1,11), vesna_ocene, label="ocene")
plt.plot(range(1,11), [po] * 10, color="r", label="prosek")
plt.title("Vesnine ocene iz informatike")
plt.legend()
plt.show()
plt.close()

Čemu služi naredba plt.figure(figsize=(15,7))?
Čemu služi funkcija range?
Čemu služi naredba legend? Kakve ona ima veze sa parametrom label u funkcijama bar i plot?
Kako bi promenio dimenzije grafikona tako da on bude kvadratnog oblika?
Kako bi promenio boju stubića u zelenu?
Šta znači izraz [po] * 10 i čemu on služi u programu?
Kako bi uklonio legendu sa grafikona?

Zadatak 5. Prikaži histogramom Petrove ocene iz informatike jednom bojom (to je onaj Petar iz Zadatka 3), njegovu prosečnu ocenu iz informatike drugom bojom, a medijanu njegovih ocena trećom bojom. Napravi legendu na dijagramu.

Zadatak 6. Prvih deset mesta na ATP listi na dan 21.7.2019. izgleda ovako:

teniseri = ["Đoković", "Nadal", "Federer", "Thiem", "Zverev", "Tsipras", "Nishikori", "Khachanov", "Fognini", "Medvedev"]
poeni    = [12415,      7945,    7460,      4595,   4325,     4045,       4040,        2890,        2785,      2625]

(a) Prikaži histogramom podatke o ATP poenima prvih deset tenisera na svetu, a crvenom linijom prikaži prosečan broj poena prvih deset igrača na ATP listi.

(b) Koliko od njih je iznad proseka?

Zadatak 7. U Zadatku 4 su date Vesnine ocene iz informatike. Histogramom prikaži koliko svaka od ocena odstupa od proseka. Sledeći Pajton programčić će ti pomoći:

odstupanje = [0] * len(vesna_ocene) # ovim smo napravili niz nula, samo da rezervišemo prostor
for i in range(len(vesna_ocene)):
    odstupanje[i] = vesna_ocene[i] - po

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