Questions: b. Construct a cumulative percentage distribution. Difference in Length Cumulative Percentage -0.005 % -0.003 % -0.001 % 0.001 % 0.003 % 0.005 %

Solution Steps

Let the frequencies of each difference in length be defined as follows: \[ \text{frequencies} = [5, 10, 15, 20, 25, 30] \]

Calculate the cumulative frequencies by summing the frequencies sequentially: \[ \begin{align_} \text{Cumulative Frequency}_1 & = 5 \\ \text{Cumulative Frequency}_2 & = 5 + 10 = 15 \\ \text{Cumulative Frequency}_3 & = 15 + 15 = 30 \\ \text{Cumulative Frequency}_4 & = 30 + 20 = 50 \\ \text{Cumulative Frequency}_5 & = 50 + 25 = 75 \\ \text{Cumulative Frequency}_6 & = 75 + 30 = 105 \\ \end{align_} \]

Determine the total frequency by summing all individual frequencies: \[ \text{Total Frequency} = 5 + 10 + 15 + 20 + 25 + 30 = 105 \]

Convert the cumulative frequencies into cumulative percentages using the formula: \[ \text{Cumulative Percentage}_i = \left( \frac{\text{Cumulative Frequency}_i}{\text{Total Frequency}} \right) \times 100 \] Calculating each cumulative percentage: \[ \begin{align_} \text{Cumulative Percentage}_1 & = \left( \frac{5}{105} \right) \times 100 = \frac{500}{105} \\ \text{Cumulative Percentage}_2 & = \left( \frac{15}{105} \right) \times 100 = \frac{1500}{105} \\ \text{Cumulative Percentage}_3 & = \left( \frac{30}{105} \right) \times 100 = \frac{3000}{105} \\ \text{Cumulative Percentage}_4 & = \left( \frac{50}{105} \right) \times 100 = \frac{5000}{105} \\ \text{Cumulative Percentage}_5 & = \left( \frac{75}{105} \right) \times 100 = \frac{7500}{105} \\ \text{Cumulative Percentage}_6 & = \left( \frac{105}{105} \right) \times 100 = 100 \\ \end{align_} \]

Final Answer