1. We are given a frequency distribution table with class intervals (Klasse) and frequencies (ni). We need to calculate the midpoints (mi), relative frequencies (fi), cumulative frequencies (cni), and cumulative relative frequencies (cfi), rounding to 2 decimal places. 2. First, calculate the total frequency $N$ by summing all $n_i$: $$N = 1 + 5 + 14 + 20 + 6 + 2 + 2 = 50$$ 3. Calculate midpoints $m_i$ for each class interval by averaging the lower and upper bounds: - $[2,8[$ midpoint: $\frac{2 + 8}{2} = 5$ - $[8,14[$ midpoint: $\frac{8 + 14}{2} = 11$ - $[14,20[$ midpoint: $\frac{14 + 20}{2} = 17$ - $[20,26[$ midpoint: $\frac{20 + 26}{2} = 23$ - $[26,32[$ midpoint: $\frac{26 + 32}{2} = 29$ - $[32,38[$ midpoint: $\frac{32 + 38}{2} = 35$ - $[38,44[$ midpoint: $\frac{38 + 44}{2} = 41$ 4. Calculate relative frequencies $f_i = \frac{n_i}{N}$ and round to 2 decimals: - $f_1 = \frac{1}{50} = 0.02$ - $f_2 = \frac{5}{50} = 0.10$ - $f_3 = \frac{14}{50} = 0.28$ - $f_4 = \frac{20}{50} = 0.40$ - $f_5 = \frac{6}{50} = 0.12$ - $f_6 = \frac{2}{50} = 0.04$ - $f_7 = \frac{2}{50} = 0.04$ 5. Calculate cumulative frequencies $cni$ by summing frequencies up to each class: - $cni_1 = 1$ - $cni_2 = 1 + 5 = 6$ - $cni_3 = 6 + 14 = 20$ - $cni_4 = 20 + 20 = 40$ - $cni_5 = 40 + 6 = 46$ - $cni_6 = 46 + 2 = 48$ - $cni_7 = 48 + 2 = 50$ 6. Calculate cumulative relative frequencies $cfi$ by summing relative frequencies up to each class and rounding to 2 decimals: - $cfi_1 = 0.02$ - $cfi_2 = 0.02 + 0.10 = 0.12$ - $cfi_3 = 0.12 + 0.28 = 0.40$ - $cfi_4 = 0.40 + 0.40 = 0.80$ - $cfi_5 = 0.80 + 0.12 = 0.92$ - $cfi_6 = 0.92 + 0.04 = 0.96$ - $cfi_7 = 0.96 + 0.04 = 1.00$ Final completed table: | Klasse | ni | mi | fi | cni | cfi | |--------|----|----|----|-----|-----| | [2,8[ | 1 | 5 | 0.02 | 1 | 0.02 | | [8,14[ | 5 | 11 | 0.10 | 6 | 0.12 | | [14,20[| 14 | 17 | 0.28 | 20 | 0.40 | | [20,26[| 20 | 23 | 0.40 | 40 | 0.80 | | [26,32[| 6 | 29 | 0.12 | 46 | 0.92 | | [32,38[| 2 | 35 | 0.04 | 48 | 0.96 | | [38,44[| 2 | 41 | 0.04 | 50 | 1.00 |