1. We are given a frequency distribution table with values $x_i$ and frequencies $f_i$ and need to calculate the relative frequency ($rf_i$ in %), cumulative frequency ($cf_i$), and cumulative relative frequency ($crf_i$ in %). 2. The total frequency $N$ is given as 50. 3. The formulas are: - Relative frequency: $$rf_i = \frac{f_i}{N} \times 100$$ - Cumulative frequency: $$cf_i = \sum_{k=0}^i f_k$$ - Cumulative relative frequency: $$crf_i = \sum_{k=0}^i rf_k$$ 4. Calculate $rf_i$ for each $f_i$: - For $f_0=0$: $$rf_0 = \frac{0}{50} \times 100 = 0\%$$ - For $f_1=5$: $$rf_1 = \frac{5}{50} \times 100 = 10\%$$ - For $f_2=7$: $$rf_2 = \frac{7}{50} \times 100 = 14\%$$ - For $f_3=8$: $$rf_3 = \frac{8}{50} \times 100 = 16\%$$ - For $f_4=4$: $$rf_4 = \frac{4}{50} \times 100 = 8\%$$ - For $f_5=4$: $$rf_5 = \frac{4}{50} \times 100 = 8\%$$ - For $f_6=7$: $$rf_6 = \frac{7}{50} \times 100 = 14\%$$ - For $f_7=9$: $$rf_7 = \frac{9}{50} \times 100 = 18\%$$ - For $f_8=6$: $$rf_8 = \frac{6}{50} \times 100 = 12\%$$ 5. Calculate cumulative frequency $cf_i$: - $cf_0 = 0$ - $cf_1 = 0 + 5 = 5$ - $cf_2 = 5 + 7 = 12$ - $cf_3 = 12 + 8 = 20$ - $cf_4 = 20 + 4 = 24$ - $cf_5 = 24 + 4 = 28$ - $cf_6 = 28 + 7 = 35$ - $cf_7 = 35 + 9 = 44$ - $cf_8 = 44 + 6 = 50$ 6. Calculate cumulative relative frequency $crf_i$: - $crf_0 = 0\%$ - $crf_1 = 0 + 10 = 10\%$ - $crf_2 = 10 + 14 = 24\%$ - $crf_3 = 24 + 16 = 40\%$ - $crf_4 = 40 + 8 = 48\%$ - $crf_5 = 48 + 8 = 56\%$ - $crf_6 = 56 + 14 = 70\%$ - $crf_7 = 70 + 18 = 88\%$ - $crf_8 = 88 + 12 = 100\%$ Final table: | $x_i$ | $f_i$ | $rf_i$ (%) | $cf_i$ | $crf_i$ (%) | |-------|-------|------------|--------|-------------| | 0 | 0 | 0 | 0 | 0 | | 1 | 5 | 10 | 5 | 10 | | 2 | 7 | 14 | 12 | 24 | | 3 | 8 | 16 | 20 | 40 | | 4 | 4 | 8 | 24 | 48 | | 5 | 4 | 8 | 28 | 56 | | 6 | 7 | 14 | 35 | 70 | | 7 | 9 | 18 | 44 | 88 | | 8 | 6 | 12 | 50 | 100 |