EDEXCEL GCSE FOUNDATION MATHS - What is Estimated Mean

Edexcel GCSE Foundation Maths: Estimated Mean

Introduction

The estimated mean is a way to find the average of a set of data when you don't have the exact values for each piece of data. It is often used when working with grouped data, where data is organized into intervals or classes.

How to Calculate Estimated Mean

1. Find the midpoints of each class interval: The midpoint of a class interval is the average of its upper and lower boundaries.
2. Multiply each midpoint by the frequency of its class: This gives you the "weighted" value of each midpoint.
3. Sum the weighted values from all classes: This gives you the total "weighted" value of the data.
4. Divide the total "weighted" value by the total frequency: This gives you the estimated mean.

Formula

Estimated Mean = (?(midpoint × frequency)) / ?(frequency) 

Where:

• ? represents the sum of
• Midpoint is the midpoint of each class interval
• Frequency is the number of data points in each class interval

Example

Step 1: Find the midpoints of each class interval.

Step 2: Multiply each midpoint by its frequency.

Step 3: Sum the weighted values. 75 + 200 + 420 + 315 = 1010

Step 4: Divide the sum by the total frequency. 1010 / 32 = 31.56

Therefore, the estimated mean of this data set is 31.56.

Key Points

• The estimated mean is an approximation of the true mean.
• The accuracy of the estimated mean depends on the size of the class intervals. Smaller intervals generally lead to a more accurate estimate.
• The estimated mean is a useful tool for analyzing grouped data and understanding the central tendency of a dataset.