Xi	Fi
9	5
4	4
5	3
9	7
9	1
Cari Nilai Standar Deviasi(Simpangan Baku) ?
*) 2 desimal,  gunakan "." (titik) bukan "," (koma)

Untuk menghitung standar deviasi (simpangan baku), kita akan menggunakan langkah-langkah berikut:

1. Hitung rata-rata \(\bar{X}\).
2. Hitung deviasi setiap nilai \(X_i\) terhadap rata-rata \((X_i - \bar{X})\).
3. Kuadratkan deviasi tersebut \((X_i - \bar{X})^2\).
4. Hitung rata-rata kuadrat deviasi tersebut (untuk populasi).
5. Ambil akar kuadrat dari hasil rata-rata kuadrat deviasi tersebut.

Langkah-langkah perhitungan:

### Data
Xi (nilai): 9, 4, 5, 9, 9  
Fi (frekuensi): 5, 4, 3, 7, 1

### Langkah 1: Hitung rata-rata (mean) \(\bar{X}\)

\[
\bar{X} = \frac{\sum (X_i \times F_i)}{\sum F_i}
\]

\[
\bar{X} = \frac{(9 \times 5) + (4 \times 4) + (5 \times 3) + (9 \times 7) + (9 \times 1)}{5 + 4 + 3 + 7 + 1}
\]

Mari kita hitung rata-ratanya.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the manual calculation if you'd like!

Here are the next steps you can follow:

1. **Calculate the numerator** for the mean:  
   Multiply each \(X_i\) by its corresponding \(F_i\), then sum them up:
   \[
   (9 \times 5) + (4 \times 4) + (5 \times 3) + (9 \times 7) + (9 \times 1)
   \]

2. **Sum up the frequencies \(F_i\)**:
   \[
   5 + 4 + 3 + 7 + 1
   \]

3. **Divide the two values** to get the mean:
   \[
   \bar{X} = \frac{\text{numerator}}{\text{sum of frequencies}}
   \]

4. Once the mean is calculated, let me know, and I can guide you through the next steps.

Would you like to proceed with these steps? Feel free to ask for further clarification.

---

Here are 5 related questions for deeper understanding:
1. What is the variance and how is it related to standard deviation?
2. How would the standard deviation change if one data point was altered significantly?
3. Can standard deviation be negative? Why or why not?
4. How is standard deviation useful in statistics and data analysis?
5. How do we interpret a low versus high standard deviation in a dataset?

**Tip**: Always double-check the frequencies and values when calculating to avoid small errors that can affect the final result.

Xi	Fi
9	5
4	4
5	3
9	7
9	1
Cari Nilai Standar Deviasi(Simpangan Baku)? *) 2 desimal, gunakan "." (titik) bukan "," (koma)

Pelajari cara menghitung standar deviasi (simpangan baku) dari data Xi dan Fi dengan langkah-langkah rinci. Termasuk konsep utama dalam statistik seperti rata-rata dan standar deviasi. Cocok untuk siswa di kelas 9-11.

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