1. **Stel het probleem vast:** We hebben een frequentietabel met waarden $x_i$ en frequenties $f_i$. We moeten de relatieve frequenties ($rf_i$), cumulatieve frequenties ($cf_i$) en cumulatieve relatieve frequenties ($crf_i$) berekenen. 2. **Formules:** - Relatieve frequentie: $$rf_i = \frac{f_i}{n} \times 100\%$$ waarbij $n$ de totale frequentie is. - Cumulatieve frequentie: $$cf_i = \sum_{j=0}^i f_j$$ - Cumulatieve relatieve frequentie: $$crf_i = \sum_{j=0}^i rf_j$$ 3. **Gegeven:** Totale frequentie $n = 50$. 4. **Bereken relatieve frequenties ($rf_i$):** - $rf_0 = \frac{0}{50} \times 100 = 0\%$ - $rf_1 = \frac{5}{50} \times 100 = 10\%$ - $rf_2 = \frac{7}{50} \times 100 = 14\%$ - $rf_3 = \frac{8}{50} \times 100 = 16\%$ - $rf_4 = \frac{4}{50} \times 100 = 8\%$ - $rf_5 = \frac{4}{50} \times 100 = 8\%$ - $rf_6 = \frac{7}{50} \times 100 = 14\%$ - $rf_7 = \frac{9}{50} \times 100 = 18\%$ - $rf_8 = \frac{6}{50} \times 100 = 12\%$ 5. **Bereken cumulatieve frequenties ($cf_i$):** - $cf_0 = 0$ - $cf_1 = 0 + 5 = 5$ - $cf_2 = 5 + 7 = 12$ - $cf_3 = 12 + 8 = 20$ - $cf_4 = 20 + 4 = 24$ - $cf_5 = 24 + 4 = 28$ - $cf_6 = 28 + 7 = 35$ - $cf_7 = 35 + 9 = 44$ - $cf_8 = 44 + 6 = 50$ 6. **Bereken cumulatieve relatieve frequenties ($crf_i$):** - $crf_0 = 0\%$ - $crf_1 = 0 + 10 = 10\%$ - $crf_2 = 10 + 14 = 24\%$ - $crf_3 = 24 + 16 = 40\%$ - $crf_4 = 40 + 8 = 48\%$ - $crf_5 = 48 + 8 = 56\%$ - $crf_6 = 56 + 14 = 70\%$ - $crf_7 = 70 + 18 = 88\%$ - $crf_8 = 88 + 12 = 100\%$ **Antwoord:** | $x_i$ | $f_i$ | $rf_i$ (%) | $cf_i$ | $crf_i$ (%) | |-------|-------|------------|--------|-------------| | 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 |