Math Problem Statement

The image contains a set of questions related to statistical analysis for a dataset involving daily sales of a food product. The tasks include determining the range, number of classes, class width, and class boundaries.

Solution

The image contains a set of questions related to statistical analysis for a dataset involving daily sales of a food product. Here's a breakdown of the tasks:

a. Determine the Range (Jangkauan)

The range is calculated as the difference between the maximum and minimum values in the dataset.

J=XmaxXminJ = X_{\text{max}} - X_{\text{min}}

Based on the numbers in the dataset, the maximum value appears to be 97 and the minimum value is 60.

J=9760=37J = 97 - 60 = 37

b. Determine the Number of Classes (Interval Kelas)

To determine the number of classes (k), use the formula:

k=1+3.3log(n)k = 1 + 3.3 \log(n)

Where n is the number of data points. Let's count the data points in your dataset:

  • You have 30 data points (since there are 30 values in the list).

Substituting into the formula:

k=1+3.3log(30)1+3.3×1.477=1+4.875.87k = 1 + 3.3 \log(30) \approx 1 + 3.3 \times 1.477 = 1 + 4.87 \approx 5.87

Therefore, round up to 6 classes.

c. Determine the Class Width (P)

To calculate the class width (P), use the formula:

P=JkP = \frac{J}{k}

Substituting the previously calculated values:

P=3766.17P = \frac{37}{6} \approx 6.17

So, the class width is approximately 6.

d. Determine the Class Boundaries (Batas Kelas)

The class boundaries are calculated as:

Lower Bound=Lowest Value0.5\text{Lower Bound} = \text{Lowest Value} - 0.5 Upper Bound=Highest Value+0.5\text{Upper Bound} = \text{Highest Value} + 0.5

For your dataset:

  • Lower Bound = 60 - 0.5 = 59.5
  • Upper Bound = 97 + 0.5 = 97.5

Would you like further help with filling out the table or explanations on how to calculate the frequency and class intervals? Let me know if you have any questions!

Here are 5 related questions you might find useful:

  1. How can I calculate the frequency distribution for this dataset?
  2. What is the difference between frequency and cumulative frequency?
  3. How can I calculate the mean from the frequency table?
  4. What is the purpose of determining the class width in data analysis?
  5. How do you interpret the range and its significance in statistics?

Tip: When rounding the number of classes, always ensure you round up to the nearest whole number to ensure you have sufficient intervals for your data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Data Analysis
Frequency Distribution

Formulas

Range: J = X_max - X_min
Number of Classes: k = 1 + 3.3 * log(n)
Class Width: P = J / k
Class Boundaries: Lower Bound = X_min - 0.5, Upper Bound = X_max + 0.5

Theorems

Frequency Distribution Theorem

Suitable Grade Level

Grades 9-12