Question

A DISTRIBUIÇÃO DE NOTAS DE UMA TURMA É FORNECIDA PELA TABELA: Frequência, Moda.

Answer 1

Explicação passo-a-passo:

a) Variável quantitativa

b)

$\sf \Big|~~~notas~~~~\Big|~~~~freq.~~~~~\Big|~~~~~~freq.~ab.~~~~\Big|~~~~~~freq.~~~~~~~\Big|~~~~~~freq.~rel.~~~~\Big|$

$\sf \Big|~(classes)~\Big|~~absoluta~\Big|~~~acumulada~~~\Big|~~~~relativa~~~~\Big|~~~~acumulada~~~\Big|$

$\sf \Big|~~2~|-~4~~~\Big|~~~~~~~3~~~~~~~\Big|~~~~~~~~~~~3~~~~~~~~~~~\Big|~~~~~3,80\%~~~~\Big|~~~~~~~3,80\%~~~~~~~\Big|$

$\sf \Big|~~4~|-~6~~~\Big|~~~~~~~7~~~~~~~\Big|~~~~~~~~~~10~~~~~~~~~~\Big|~~~~~8,86\%~~~~\Big|~~~~~~12,66\%~~~~~~\Big|$

$\sf \Big|~~6~|-~8~~~\Big|~~~~~~45~~~~~~\Big|~~~~~~~~~~55~~~~~~~~~~\Big|~~~~56,96\%~~~\Big|~~~~~~69,62\%~~~~~~\Big|$

$\sf \Big|~~8~|-~10~\Big|~~~~~~24~~~~~~\Big|~~~~~~~~~~79~~~~~~~~~~\Big|~~~~30,38\%~~~\Big|~~~~~~~~100\%~~~~~~~\Big|$

c)

=> Média

$\sf M=\dfrac{3\cdot3+7\cdot5+45\cdot7+24\cdot9}{3+7+45+24}$

$\sf M=\dfrac{9+35+315+216}{79}$

$\sf M=\dfrac{575}{79}$

$\sf \red{M=7,28}$

=> Mediana

A mediana é valor central, quando colocamos os valores em ordem crescente

Como há 79 valores, o central é o $\sf \dfrac{79+1}{2}=\dfrac{80}{2}=40°$ valor

Temos $\sf 3+7=10$. Assim, 10 estudantes tiraram menos de 6

E $\sf 3+7+45=55$. Note que já passamos de 45. A mediana pertence à classe 6 |– 8.

Logo, a mediana é o ponto médio dessa classe, ou seja, $\sf \dfrac{6+8}{2}=\dfrac{14}{2}=7$

A mediana é 7

=> Moda

É o valor que mais se repete. Note que a classe com a maior frequência é 6 |– 8, então a moda é ponto médio dessa classe, isto é, $\sf \dfrac{6+8}{2}=\dfrac{14}{2}=7$

A moda é 7

d)

=> Variância

$\sf \sigma^2=\dfrac{3\cdot(3-7,28)^2+7\cdot(5-7,28)^2+45\cdot(7-7,28)^2+24\cdot(9-7,28)^2}{79}$

$\sf \sigma^2=\dfrac{3\cdot(-4,28)^2+7\cdot(-2,28)^2+45\cdot(-0,28)^2+24\cdot1,72^2}{79}$

$\sf \sigma^2=\dfrac{3\cdot18,3184+7\cdot5,1984+45\cdot0,0784+24\cdot2,9584}{79}$

$\sf \sigma^2=\dfrac{54,9552+36,3888+3,528+71,0016}{79}$

$\sf \sigma^2=\dfrac{165,8736}{79}$

$\sf \red{\sigma^2=2,099}$

=> Desvio padrão

$\sf \sigma=\sqrt{\sigma^2}$

$\sf \sigma=\sqrt{2,099}$

$\sf \red{\sigma=1,448}$

=> Coeficiente de variação

$\sf CV\%=\dfrac{\sigma}{M}\cdot100$

$\sf CV\%=\dfrac{1,448}{7,28}\cdot100$

$\sf CV\%=\dfrac{144,8}{7,28}$

$\sf CV\%=\dfrac{14480}{728}$

$\sf \red{CV\%=19,89\%}$

Média dispersão