Averages from tables 1 (Edexcel GCSE Maths): Revision Notes
Averages from tables 1
When working with frequency tables, you need to be extremely careful about what the numbers represent. Frequency tells you how many pieces of data have a particular value - it's not the actual data value itself.
Understanding frequency tables
A frequency table shows:
- The data values in one column
- How often each value occurs (frequency) in another column
The key thing to remember is that frequency is not a data value - it tells you the number of pieces of data with a given value.
Calculating the mode from a frequency table
The mode is the value that appears most frequently in the data set.
Method:
- Look at the frequency column
- Find the highest frequency
- The mode is the data value that corresponds to this highest frequency
Worked Example: Finding the Mode
In a table showing pet ownership, if 18 people own 1 pet (highest frequency), then the mode is 1 pet.
Calculating the range from a frequency table
The range is the difference between the highest and lowest data values.
Method:
- Identify the highest data value in the table
- Identify the lowest data value in the table
- Calculate: Range = Highest value - Lowest value
Worked Example: Calculating Range
If the data values go from 0 pets to 4 pets, then: Range = 4 - 0 = 4 pets
Calculating the median from a frequency table
The median is the middle value when all data values are arranged in order.
Method:
- Add up all the frequencies to find the total number of data values
- Find the position of the median (if n values total, median is between the th and th values)
- Count through the frequencies until you reach this middle position
- The median is the data value at this position
Worked Example: Finding the Median
With 40 people surveyed, the median is between the 20th and 21st values.
If the first 12 values are 0, and the next 18 values are all 1, then both the 20th and 21st values are 1.
Therefore, the median is 1 pet.
Calculating the mean from a frequency table
The mean is the average value, calculated using all data values and their frequencies.
Method:
- Create an extra column: Frequency × data value (f × x)
- Multiply each data value by its frequency
- Add up all values in the f × x column
- Add up all frequencies
- Calculate:
Do not round your final answer unless specifically asked.
Worked Example: Calculating the Mean
Step 1: Create the f × x column and calculate totals
- Total of f × x column = 0 + 18 + 14 + 6 + 4 = 42
- Total frequency = 12 + 18 + 7 + 2 + 1 = 40
Step 2: Apply the formula Mean = = 1.05 pets
Exam Tips
- Students often struggle with median calculations from frequency tables in exams
- Always check you're using data values, not frequencies, in your calculations
- For mean calculations, always show your working with the f × x column
- Don't round your mean unless the question asks you to
Key Points to Remember:
- Mode = data value with the highest frequency, not the frequency itself
- Range = highest data value minus lowest data value
- Median = middle value found by counting through frequencies to the middle position
- Mean = total of (f × x) column divided by total frequency
- Always create an extra f × x column when calculating the mean from a frequency table