Math Problem Statement

Hitung nilai rata-rata data berkelompok di bawah ini dengan menggunakan cara 'tanda-kelas'.

Solution

The problem provided is asking to calculate the mean (average) of grouped data using the class-mark method ("tanda-kelas" in Indonesian).

The table includes:

  • Class intervals (Kelas interval): These are the ranges of values.
  • Frequency (f): This represents the number of occurrences for each class interval.

Step-by-Step Solution

  1. Calculate Class Mark (tanda-kelas): The class mark for each interval is the midpoint, calculated as:

    Class mark=Lower limit+Upper limit2\text{Class mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2}

  2. Multiply Frequency (f) by Class Mark: Multiply the frequency of each interval by the corresponding class mark.

  3. Calculate Mean: The formula for the mean is:

    xˉ=(f×x)f\bar{x} = \frac{\sum (f \times x)}{\sum f} where:

    • ff is the frequency.
    • xx is the class mark.
    • f\sum f is the total frequency.

Calculations:

No urutKelas intervalffClass Mark xxf×xf \times x
120 - 24220+242=22\frac{20+24}{2} = 222×22=442 \times 22 = 44
225 - 29525+292=27\frac{25+29}{2} = 275×27=1355 \times 27 = 135
330 - 341330+342=32\frac{30+34}{2} = 3213×32=41613 \times 32 = 416
435 - 391735+392=37\frac{35+39}{2} = 3717×37=62917 \times 37 = 629
540 - 441740+442=42\frac{40+44}{2} = 4217×42=71417 \times 42 = 714
645 - 49645+492=47\frac{45+49}{2} = 476×47=2826 \times 47 = 282

f=60,(f×x)=2220\sum f = 60, \quad \sum (f \times x) = 2220

Mean Calculation:

xˉ=222060=37\bar{x} = \frac{2220}{60} = 37

So, the mean of the grouped data is 37.

Would you like further details or clarification?

Here are 5 related questions you could explore:

  1. What is the importance of using class marks in grouped data?
  2. How would the mean change if the class intervals were different but the frequencies stayed the same?
  3. How can we calculate the mode and median for this grouped data?
  4. What is the difference between grouped and ungrouped data in statistics?
  5. How does the class width affect the accuracy of the calculated mean?

Tip: Always double-check your class marks and frequency products to avoid simple calculation errors when dealing with grouped data.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Grouped Data
Class Mark

Formulas

Class mark (tanda-kelas) = (Lower limit + Upper limit) / 2
Mean (average) = Σ(f × x) / Σf

Theorems

-

Suitable Grade Level

Grades 10-12