Math Problem Statement

Find the median for the given frequency distribution.

Solution

To find the median of a frequency distribution, we need to determine the cumulative frequency and then locate the median class.

Step-by-Step Solution:

1. Organize the Data

Given dataTo find the median of a frequency distribution, we need to determine the cumulative frequency and then locate the median class.

Step-by-Step Solution:

1. Organize the Data

Given

  • Values (x): 2, 4, 6, 8, 10
  • Frequencies (f): 12, 8, 5, 1, 2

2. Calculate the Total Frequency (N)

Sum of all frequencies: N=12+8+5+1+2=28N = 12 + 8 + 5 + 1 + 2 = 28

3. Find the Cumulative Frequency (cf)

The cumulative frequency table is:

  • For x=2x = 2: cf=12cf = 12
  • For x=4x = 4: cf=12+8=20cf = 12 + 8 = 20
  • For x=6x = 6: cf=20+5=25cf = 20 + 5 = 25
  • For x=8x = 8: cf=25+1=26cf = 25 + 1 = 26
  • For x=10x = 10: cf=26+2=28cf = 26 + 2 = 28

4. Determine the Median Position

The median position in the cumulative frequency is at N2=282=14\frac{N}{2} = \frac{28}{2} = 14.

5. Identify the Median Class

We look for the cumulative frequency that reaches or just exceeds 14. In this case:

  • cf=12cf = 12 for x=2x = 2
  • cf=20cf = 20 for x=4x = 4

Since 14 lies between 12 and 20, the median class corresponds to x=4x = 4.

Answer

The median value is: Median=4\text{Median} = 4

Would you like more details on the calculation steps or have further questions?

Related Questions

  1. How would you find the mode in a frequency distribution?
  2. How is the median different from the mean in a data set?
  3. What is the importance of cumulative frequency in statistics?
  4. How would you calculate the median if the data had an odd total frequency?
  5. Can the median be a non-integer in frequency distributions?

Tip

For frequency distributions, the median class is identified based on cumulative frequency, rather than raw frequency values.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Cumulative Frequency
Median

Formulas

Median position = N/2
Cumulative frequency

Theorems

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Suitable Grade Level

Grades 8-10