Mean, median, mode and range: find the missing number

key notes :

🔢 Mean (Average)

Definition: The mean is the sum of all numbers divided by the total number of values.

To find a missing number:

• Multiply the mean by the number of values to get the total sum.Subtract the known values’ sum from the total to find the missing number.

Example:
Mean = 6; Numbers: 4, 6, __, 8
Total = 6 × 4 = 24
Known sum = 4 + 6 + 8 = 18
Missing number = 24 – 18 = 6

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🟰 Median

Definition: The median is the middle number in an ordered list.

Steps to find a missing number:

• Arrange the values (including a placeholder for the missing one).
• Use the position of the median to set up an equation.
• Solve for the missing number.

Example:
Numbers: 3, __, 7
Median = 5
So the list becomes: 3, __, 7
To get a median of 5, the missing number must be 5.

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🧮 Mode

Definition: The mode is the number that appears most often.

To find the missing number:

• Check the frequency of each number.
• Set the missing number so that it matches the mode requirement.

Example:
Numbers: 2, 4, 4, __, 6
Mode = 4
So the missing number should not appear more than twice, or must be another 4 to increase the mode’s frequency.

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📏 Range

Definition: The range is the difference between the highest and lowest numbers. Range=Highest−Lowest

To find the missing number:

• Use the given range and known values to set up an equation.

Example:
Numbers: 3, 6, 8, __
Range = 7
If __ is the highest:
__ – 3 = 7 → Missing number = 10

Learn with an example

let’s practice!