Averages from tables 2 Revision Notes for Edexcel GCSE Maths

Averages from tables 2

What are class intervals?

Sometimes data in a frequency table is organised into class intervals. This means the data is grouped into ranges rather than showing individual values. When data is grouped this way, you don't know the exact data values, so you can only calculate estimates of the mean.

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Class intervals are particularly useful when dealing with large datasets or when precise individual values aren't necessary for analysis. The trade-off is that we lose some precision in our calculations.

Finding the modal class interval

The modal class interval is the class interval that contains the mode. This is simply the class interval with the highest frequency.

To identify the modal class interval:

Look at the frequency column
Find the highest frequency value
The corresponding class interval is your modal class interval

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Don't confuse the modal class interval with the actual mode value. The modal class interval is just the range where the mode is located, not the exact mode value itself.

Finding the median class interval

The median class interval is the class interval that contains the median value. This is found by:

Working out the median position using $(n + 1) \div 2$
Finding which class interval this position falls into
This class interval contains the median

Estimating the mean from grouped data

When data is grouped into class intervals, you need to use the mid-point method to estimate the mean.

Step-by-step method

Step 1: Add extra columns to your table

Add a 'Mid-point (x)' column
Add a 'f × x' column

Step 2: Calculate the mid-point of each class interval

Mid-point = (lowest value + highest value) ÷ 2
For example: class interval $20 \leq t < 40$ has mid-point $(20 + 40) \div 2 = 30$

Step 3: Calculate f × x for each row

Multiply the frequency by the mid-point for each class interval

Step 4: Find the totals

Sum all values in the f × x column
Sum all frequencies

Step 5: Calculate the estimated mean

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Key Formula: $\text{Estimated mean} = \frac{\text{Total of (f × x column)}}{\text{Total frequency}}$

Why is this an estimate?

Your answer is an estimate because you don't know the exact data values within each class interval. You're assuming all values in each interval equal the mid-point, which may not be true.

Worked example breakdown

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Worked Example: Travel Time Data Analysis

Looking at travel time data:

Modal class interval: $0 \leq t < 20$ (frequency = 65, the highest)
Median class interval: $20 \leq t < 40$ (contains the median position)
Estimated mean calculation:

Step-by-step calculation:

Sum of f × x = 650 + 1260 + 1950 + 280 = 4140
Total frequency = 65 + 42 + 39 + 4 = 150
Estimated mean = $4140 \div 150 = 27.6$ minutes

Therefore, the estimated mean travel time is 27.6 minutes.

Exam tips

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Exam Success Tips:

Always label your answer as an "estimate" when working with grouped data
Show your working clearly by adding the extra columns
Double-check your mid-point calculations
Remember to divide by the total frequency, not the number of class intervals

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Key Points to Remember:

Modal class interval = class interval with the highest frequency
Median class interval = class interval containing the median position
Estimated mean = Total of (f × x) ÷ Total frequency
Use mid-points when exact values are unknown in class intervals
Your answer is always an estimate because you don't know the exact data values

Averages from tables 2 (Edexcel GCSE Maths): Revision Notes