Math Problem Statement

Manajer Bengkel Alsintan ingin melihat distribusi biaya perbaikan traktor tangan. Hitunglah nilai tengah, modus, rata-rata, simpangan baku, dan koefisien keragaman dari data biaya perbaikan yang diberikan. Selain itu, berapa peluang biaya perbaikan berada dalam rentang rata-rata ± simpangan baku?

Solution

From the image you uploaded, the problem is asking for statistical analysis of repair costs for tractors in an agricultural machinery workshop. Here is a breakdown of the questions:

  1. First Question: You are required to calculate the following from the provided dataFrom the image you uploaded, the problem is asking for statistical analysis of repair costs for tractors in an agricultural machinery workshop. Here is a breakdown of the questions:

  2. First Question: You are required to calculate the following from the provided

    • Median (Nilai Tengah)
    • Mode (Modus)
    • Mean (Rata-rata)
    • Standard Deviation (SD)
    • Coefficient of Variation (Koefisien Keragaman or KK)
  3. Second Question: The probability of the repair cost falling within the range defined by the mean plus or minus one standard deviation (i.e., between μσ\mu - \sigma and μ+σ\mu + \sigma).

Let me first extract the relevant data from the table and calculate these statistics. I will start by calculating the median, mode, mean, standard deviation, and the coefficient of variation. Then I'll compute the probability in the second part.Here are the calculated values based on the provided dataHere are the calculated values based on the provided

  1. Mean (Rata-rata): 84.65
  2. Median (Nilai Tengah): 86.5
  3. Mode (Modus): 85
  4. Standard Deviation (SD): 12.19
  5. Coefficient of Variation (Koefisien Keragaman): 14.40%

Now, I'll calculate the probability of the repair cost falling within the range of one standard deviation from the mean (i.e., between μσ\mu - \sigma and μ+σ\mu + \sigma).The range defined by one standard deviation from the mean is approximately between:

  • Lower Bound: 72.46
  • Upper Bound: 96.84

The probability of the repair cost falling within this range is 62.5%.

Let me know if you need any further details or clarification.

Here are 5 related questions to expand on this topic:

  1. How do you calculate the variance from the given data?
  2. What is the significance of the coefficient of variation (KK) in this context?
  3. How would the result change if we considered population standard deviation instead of sample standard deviation?
  4. How can we interpret the mode in a dataset like this one, where multiple values are similar?
  5. How does the empirical rule (68-95-99.7 rule) relate to this probability calculation?

Tip: When analyzing data, it’s essential to understand whether you're working with a sample or an entire population. This distinction affects calculations like standard deviation and variance.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Probability

Formulas

Mean (Rata-rata): (sum of all data points) / (number of data points)
Median (Nilai Tengah): Middle value when data is sorted
Mode (Modus): Most frequent value in the dataset
Standard Deviation (Simpangan Baku): sqrt((Σ(xi - μ)²) / (n - 1))
Coefficient of Variation (Koefisien Keragaman): (SD / Mean) * 100

Theorems

Empirical Rule (68-95-99.7 Rule)

Suitable Grade Level

University level, Statistics course