Example 2

13.4.3 Example 2

Description

Quick Overview

This section provides an example illustrating how to compute the median of grouped data.

Standard

The focus of this section is on Example 8, where the median of a frequency distribution is determined. The solution explores the relationships between the values in the distribution and makes use of cumulative frequency to accurately calculate the median.

Detailed

Example 8: Finding the Median of Grouped Data

In this example, we are given a frequency distribution with multiple class intervals, and we are tasked with finding the median value when the total number of observations equals 100. This problem demonstrates the application of the median formula for grouped data, which involves cumulative frequencies and identifying the median class.

As we progress through the example, we identify crucial variables: the lower limit of the median class (l), the cumulative frequency (cf) of the class preceeding the median class, the frequency (f) of the median class, and the total number of observations (n). Using these elements, we implement the median formula:

$$ Median = l + \frac{n/2 - cf}{f} \times h $$

In doing so, we observe that the selected median class (500 - 600) provides relevant insights into the distribution of the data, revealing the statistical behavior and facilitating a more precise understanding of the dataset.

Key Concepts

  • Median: The value that separates the higher half from the lower half of a data sample.

  • Cumulative Frequency: The sum of frequencies of all classes up to a certain point.

  • Median Class: The class interval containing the median value of the data.

Memory Aids

🎵 Rhymes Time

  • To find the median, just look around, Half the data will be found!

📖 Fascinating Stories

  • Once upon a time, a data partying group needed to find their middle member to break the ties. They stacked their numbers from least to greatest, and along came the median to show them balance!

🧠 Other Memory Gems

  • L-N-C-F: Lower limit, Number in total, Cumulative frequency, Frequency count—remember these to find the median out!

🎯 Super Acronyms

M.E.D. = Median, Example, Distribution - Use these to calculate the median!

Examples

  • Example 1: Finding the median of a data set of students' scores.

  • Example 2: Using frequency distribution to calculate median temperature data.

Glossary of Terms

  • Term: Cumulative Frequency

    Definition:

    The sum of the frequencies that occur up to a given point in a frequency distribution.

  • Term: Median

    Definition:

    The value separating the higher half from the lower half of a data sample.

  • Term: Frequency Distribution

    Definition:

    A summary of how often different values occur within a dataset.

  • Term: Median Class

    Definition:

    The category in a grouped frequency distribution that contains the median value.

  • Term: Class Width (h)

    Definition:

    The difference between the upper and lower boundaries of a class in a frequency distribution.