Math Problem Statement

Nilai median dari data berikut adalah... Nilai: 10, 15, 20, 25, 30 Frekuensi: 2, 5, 8, 4, 1

Solution

The table shows data with values ("Nilai") and their corresponding frequencies ("Frekuensi"). To calculate the median, we need to follow these steps:

  1. Identify the total number of data points: The total number of data points is the sum of the frequencies:

    2+5+8+4+1=202 + 5 + 8 + 4 + 1 = 20

  2. Determine the position of the median: Since there are 20 data points (an even number), the median will be the average of the 10th and 11th values when the data is arranged in order.

  3. Find the cumulative frequency:

    • Cumulative frequency for value 10: 22
    • Cumulative frequency for value 15: 2+5=72 + 5 = 7
    • Cumulative frequency for value 20: 7+8=157 + 8 = 15

    The 10th and 11th data points fall within the cumulative frequency of 15, meaning they correspond to the value of 20.

  4. Conclusion: The median value is 20.

Thus, the correct answer is c. 20.


Do you want more details or have any questions?

Here are 5 related questions:

  1. How do you calculate the mean of this dataset?
  2. What is the mode of the given dataset?
  3. How would the median change if the frequency of 30 was increased?
  4. Can you explain the difference between median and mean in a dataset?
  5. How do you find the range of the data values?

Tip: The median is a measure of central tendency that is less affected by extreme values compared to the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Median
Cumulative Frequency

Formulas

Median position in an ordered dataset: (n + 1)/2 for odd datasets or average of n/2 and (n/2) + 1 positions for even datasets

Theorems

Median is the middle value in an ordered data set or the average of the two middle values in an even-sized data set

Suitable Grade Level

Grades 7-9