Uma turma de 40 alunos foi submetida a um teste com 12 problemas difíceis de a. Transforme a seguinte distribuição de escores (númeru de respostas corretas) uma distribuição frequências agrupadas contendo quatro intervalos de classe e etermine o tamanho dos intervalos de classe. dique os limites inferior e superior de cada intervalo de classe. entifique o ponto médio de cada intervalo de classe. che a frequência relativa de cada intervalo de classe. termine a frequência acumulada de cada intervalo de classe. he a frequência relativa acumulada de cada intervalo de classe. ça um histograma e um poligono de frequências.

## Step 1: Determine the Range and Class Width<br />### The range of the scores is from 1 to 12. To create four class intervals, we calculate the class width using the formula: <br />\[<br />\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{12 - 1}{4} = 2.75<br />\]<br />Since class widths are typically whole numbers, we round up to 3.<br /><br />## Step 2: Define Class Intervals<br />### With a class width of 3, the class intervals will be:<br />- Interval 1: 1 to 3<br />- Interval 2: 4 to 6<br />- Interval 3: 7 to 9<br />- Interval 4: 10 to 12<br /><br />## Step 3: Identify Midpoints of Each Interval<br />### The midpoint of each interval is calculated as follows:<br />- Interval 1: $\frac{1 + 3}{2} = 2$<br />- Interval 2: $\frac{4 + 6}{2} = 5$<br />- Interval 3: $\frac{7 + 9}{2} = 8$<br />- Interval 4: $\frac{10 + 12}{2} = 11$<br /><br />## Step 4: Calculate Frequency for Each Interval<br />### Sum the frequencies (F) within each interval:<br />- Interval 1 (1 to 3): $2 + 1 + 2 = 5$<br />- Interval 2 (4 to 6): $2 + 2 + 2 = 6$<br />- Interval 3 (7 to 9): $5 + 5 + 6 = 16$<br />- Interval 4 (10 to 12): $4 + 3 + 3 = 10$<br /><br />## Step 5: Calculate Relative Frequency for Each Interval<br />### Relative frequency is calculated by dividing the frequency of each interval by the total number of observations (n = 40):<br />- Interval 1: $\frac{5}{40} = 0.125$<br />- Interval 2: $\frac{6}{40} = 0.15$<br />- Interval 3: $\frac{16}{40} = 0.4$<br />- Interval 4: $\frac{10}{40} = 0.25$<br /><br />## Step 6: Calculate Cumulative Frequency for Each Interval<br />### Add the frequencies cumulatively:<br />- Interval 1: 5<br />- Interval 2: $5 + 6 = 11$<br />- Interval 3: $11 + 16 = 27$<br />- Interval 4: $27 + 10 = 37$<br /><br />## Step 7: Calculate Cumulative Relative Frequency for Each Interval<br />### Add the relative frequencies cumulatively:<br />- Interval 1: 0.125<br />- Interval 2: $0.125 + 0.15 = 0.275$<br />- Interval 3: $0.275 + 0.4 = 0.675$<br />- Interval 4: $0.675 + 0.25 = 0.925$<br /><br />## Step 8: Construct Histogram and Frequency Polygon<br />### A histogram can be constructed with the class intervals on the x-axis and the frequencies on the y-axis. A frequency polygon can be drawn by plotting the midpoints against their respective frequencies and connecting the points with straight lines.