Math Problem Statement

Tabel frekuensi berikut menunjukkan nilai ujian dan frekuensinya. Tentukan median dari data pada tabel tersebut.

Solution

The image contains a frequency table in Indonesian, which represents the results of an exam. The task is to find the median of the data in the table.

Values and Frequencies from the table:

  • 3 occurs 3 times
  • 4 occurs 5 times
  • 5 occurs 6 times
  • 6 occurs 8 times
  • 7 occurs 9 times
  • 8 occurs 7 times
  • 9 occurs 3 times

To calculate the median:

  1. First, we determine the total number of data points (total frequency): 3+5+6+8+9+7+3=413 + 5 + 6 + 8 + 9 + 7 + 3 = 41 So, there are 41 data points in total.

  2. The median is the middle value of the dataset, which is the 21st value (since 41 is odd, the median is at position 41+12=21\frac{41+1}{2} = 21).

  3. Now, we look at the cumulative frequency to find the 21st value:

    • Cumulative frequency up to 3: 3
    • Cumulative frequency up to 4: 3 + 5 = 8
    • Cumulative frequency up to 5: 8 + 6 = 14
    • Cumulative frequency up to 6: 14 + 8 = 22

    The 21st value is in the range where the value is 6, because the cumulative frequency reaches 22 at the value 6, which includes the 21st position.

Therefore, the median is 6.

So, the correct answer is:

  • c. 6

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Median Calculation

Formulas

Median position = (n + 1)/2, where n is the total frequency

Theorems

Frequency distribution theorem

Suitable Grade Level

Grades 7-9