Average with a Missing Value

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Given a target mean and all but one data value, solve for the missing value.

If the arithmetic mean of n values must equal M, then the total sum of the values must equal n · M. To find a missing value, compute the required total (n · M) and subtract the sum of the known values: missing = n · M − Σ(known). This technique applies whenever one item is unknown — the next test score, the final month's sales, a missing measurement — and a target average is specified.

missing = n · M − Σ(known values)

• Four test scores average 80. Three scores are 75, 82, 78. Missing = 4·80 − (75+82+78) = 320 − 235 = 85
• Five months' sales average $10,000. Four months total $38,500. Missing = 5·10000 − 38500 = $11,500
• Six measurements average 12.5. Five sum to 70. Missing = 6·12.5 − 70 = 5

How to recognize it

• A mean is given but one value is unknown
• Keywords: 'target average', 'needs to average', 'what score is required'
• The total count of values n is known

Common mistakes

• Forgetting to multiply the mean by n to get the required total
• Subtracting in the wrong order (known − total instead of total − known)
• Using n − 1 instead of n when counting the total number of values

Practice guidance

Numerical Reasoning