Subjects statistics

Mean Deviation 53942E

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1. **Stating the problem:** We are given a frequency distribution of student scores and asked to find the mean deviation (rata-rata simpangan) from the mean. 2. **Data from the table:** Nilai (x): 10, 20, 30, 40, 50, 60, 70, 80 Jumlah siswa (f): 8, 10, 15, 25, 20, 18, 9, 5 3. **Step 1: Calculate the mean ($\bar{x}$) of the data.** $$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$ Calculate total frequency: $$\sum f_i = 8 + 10 + 15 + 25 + 20 + 18 + 9 + 5 = 110$$ Calculate $\sum f_i x_i$: $$8\times10 + 10\times20 + 15\times30 + 25\times40 + 20\times50 + 18\times60 + 9\times70 + 5\times80$$ $$= 80 + 200 + 450 + 1000 + 1000 + 1080 + 630 + 400 = 4840$$ Mean: $$\bar{x} = \frac{4840}{110} = 44$$ 4. **Step 2: Calculate the absolute deviations $|x_i - \bar{x}|$ and multiply by frequencies $f_i$.** |Nilai $x_i$|Frekuensi $f_i$|$|x_i - \bar{x}|$|$f_i \times |x_i - \bar{x}|$| |---|---|---|---| |10|8|$|10 - 44| = 34$|$8 \times 34 = 272$| |20|10|$|20 - 44| = 24$|$10 \times 24 = 240$| |30|15|$|30 - 44| = 14$|$15 \times 14 = 210$| |40|25|$|40 - 44| = 4$|$25 \times 4 = 100$| |50|20|$|50 - 44| = 6$|$20 \times 6 = 120$| |60|18|$|60 - 44| = 16$|$18 \times 16 = 288$| |70|9|$|70 - 44| = 26$|$9 \times 26 = 234$| |80|5|$|80 - 44| = 36$|$5 \times 36 = 180$| Sum of $f_i \times |x_i - \bar{x}|$: $$272 + 240 + 210 + 100 + 120 + 288 + 234 + 180 = 1644$$ 5. **Step 3: Calculate the mean deviation:** $$\text{Mean Deviation} = \frac{\sum f_i |x_i - \bar{x}|}{\sum f_i} = \frac{1644}{110} = 14.9454 \approx 14.95$$ **Final answer:** 14.95