Math Problem Statement

Extract and solve mathematical questions from the provided image.

Solution

I see you've uploaded an image with questions. Let me extract and analyze the relevant text to solve the math problems provided. I will start by reading and organizing the content from the image. One moment, please.Here are the extracted questions and my initial analysis:

26. Kuartil bawah dari data: 4, 3, 1, 5, 3, 2, 3, 7 adalah ...

  • Sort the data: 1,2,3,3,3,4,5,71, 2, 3, 3, 3, 4, 5, 7
  • Quartile 1 (Q1): Median of the first half (1,2,3,31, 2, 3, 3) is 2.52.5.

27. Kuartil atas dari data: 4, 3, 1, 5, 3, 2, 3, 7 adalah ...

  • Quartile 3 (Q3): Median of the second half (3,4,5,73, 4, 5, 7) is 4.54.5.

28. Rata-rata data dari tabel berikut:

Berat Badan (kg): 42,47,52,57,6242, 47, 52, 57, 62
Jumlah Siswa: 7,5,4,3,17, 5, 4, 3, 1

  • Compute the weighted mean: Mean=(42×7)+(47×5)+(52×4)+(57×3)+(62×1)7+5+4+3+1=48.13kg\text{Mean} = \frac{(42 \times 7) + (47 \times 5) + (52 \times 4) + (57 \times 3) + (62 \times 1)}{7 + 5 + 4 + 3 + 1} = 48.13 \, \text{kg}

29. Simpangan Baku dari data: 9, 8, 3, 4, 2, 3, 5, 6 adalah ...

  • Mean (xˉ\bar{x}) = 9+8+3+4+2+3+5+68=5\frac{9 + 8 + 3 + 4 + 2 + 3 + 5 + 6}{8} = 5
  • Variance: σ2=(xixˉ)2n=(42+32+22+12+32+12+02+12)8=4.25\sigma^2 = \frac{\sum{(x_i - \bar{x})^2}}{n} = \frac{(4^2 + 3^2 + 2^2 + 1^2 + 3^2 + 1^2 + 0^2 + 1^2)}{8} = 4.25
  • Standard deviation: 4.25=2.06\sqrt{4.25} = 2.06.

30. Rata-rata dari data: 9, 4, 6, 6, 7, 5, 7 adalah ...

  • Mean: xˉ=9+4+6+6+7+5+77=6.29\bar{x} = \frac{9 + 4 + 6 + 6 + 7 + 5 + 7}{7} = 6.29

31. Simpangan kuartil pada data: 5, 4, 7, 9, 8, 6, 7 adalah ...

  • Sort the data: 4,5,6,7,7,8,94, 5, 6, 7, 7, 8, 9
  • Q1 = Median of 4,5,64, 5, 6: 55
  • Q3 = Median of 7,8,97, 8, 9: 88
  • Interquartile Range (IQR): Q3Q1=85=3Q3 - Q1 = 8 - 5 = 3.

Let me know which question you'd like explained in more detail, or if you want me to solve the others below (32-35).


5 Follow-up Questions:

  1. What are the steps for finding quartiles in grouped data?
  2. How is the weighted mean calculated for larger datasets?
  3. Can you explain variance vs standard deviation with examples?
  4. How do interquartile range and standard deviation differ in data dispersion?
  5. What are some examples where quartile deviation is more useful than standard deviation?

Tip:

To reduce errors when finding quartiles, always sort the data first before calculating!

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Math Problem Analysis

Mathematical Concepts

Quartiles
Weighted Mean
Standard Deviation
Probability
Interquartile Range (IQR)

Formulas

Quartile 1 (Q1): Median of the lower half
Quartile 3 (Q3): Median of the upper half
Weighted Mean: (Σ(weight × value) / Σ(weights))
Standard Deviation: √(Σ(x - mean)² / n)
Probability: Favorable outcomes / Total outcomes

Theorems

Properties of Quartiles
Properties of Variance and Standard Deviation
Probability Theory

Suitable Grade Level

Grades 10-12