Math Problem Statement

The median is 24, and the frequency distribution table is given. Find the missing frequency (x) using the median formula.

Solution

The image contains a frequency distribution table with cumulative frequencies (C.F.) and the median calculation using the formula for grouped data. Here's a breakdown of the steps:

Given Data:

AgeNo. of PersonsC.F.
0-1055
10-202530
20-30xx30+x30 + x
30-401848+x48 + x
40-50755+x55 + x
  • Total N=55+xN = 55 + x.
  • Median is 24, which corresponds to the class interval 203020-30.

Formula for Median:

Median=L+(N2C.F.)×hf\text{Median} = L + \left( \frac{N}{2} - C.F.\right) \times \frac{h}{f} Where:

  • L=20L = 20 (Lower boundary of the median class),
  • N=55+xN = 55 + x (Total frequency),
  • C.F.=30C.F. = 30 (Cumulative frequency before the median class),
  • h=10h = 10 (Class width),
  • f=xf = x (Frequency of the median class).

Median Calculation:

Using the formula: 24=20+(55+x230)×10x24 = 20 + \left( \frac{55 + x}{2} - 30 \right) \times \frac{10}{x}

Simplify and solve for xx.

Let me calculate that.The value of xx is 25. Therefore, the frequency of the 20-30 age group is 25.

Would you like further details on the steps or any clarifications?

Here are five related questions for further practice:

  1. What would happen to the median if the value of xx were different?
  2. How do you calculate the mean from a frequency distribution like this one?
  3. What if you were asked to calculate the mode instead of the median?
  4. How would you compute the quartiles from this data?
  5. How would you adjust the class intervals if the number of persons changed?

Tip: Always check if the total cumulative frequency NN is consistent with the sum of individual frequencies for accuracy.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Median for Grouped Data

Formulas

Median = L + ((N / 2) - C.F.) * (h / f)

Theorems

Median for Grouped Data Theorem

Suitable Grade Level

Grades 11-12