Missing Value Given the Mean | Statistics

📖 Before You Start

If you haven't already, visit the Mean, Median, Mode & Range page first. That page covers how to calculate a basic average.

This page is different. Finding a missing value when you already know the mean is a separate GED skill — because instead of calculating the average, you have to work backwards to find a number you don't have yet. Many students find this confusing because it looks like an average problem but actually works in reverse.

💡 The Key Idea — It's All About the Total

Here's the most important thing to understand: the mean is based on the total of all the numbers.

Think of all the numbers being dumped into one big pile called the total. The mean is just that total divided equally. So if you know the mean and how many numbers there are, you can figure out what the total must be — and then find what's missing.

The 3-Part Strategy:

1. Add up the numbers you already know.
2. Find what the total SHOULD be: Mean × Number of Values.
3. Subtract: Required Total − Known Total = Missing Value.

📐 The Two Formulas

You probably know the standard mean formula:

Standard Formula

Mean = Total ÷ Number of Values

This is how you calculate a mean when you have all the numbers.

Now rearrange it. If you multiply both sides by the number of values, you get:

⭐ The Key Formula for This Skill

Total = Mean × Number of Values

This tells you what all the numbers MUST add up to. Use this formula first.

⚠️ Do NOT divide first. Most students see the word "average" and immediately start dividing. For this skill, you start with multiplication. Find the required total before you do anything else.

🔢 Worked Example

Five numbers have a mean of 12. Four of the numbers are 9, 11, 14, and 10. What is the missing number?

Step-by-Step Solution

Step 1 — Add the known values: 9 + 11 + 14 + 10 = 44

Step 2 — Find the required total: 5 × 12 = 60

Step 3 — Subtract: 60 − 44 = 16

Missing number = 16

Check your answer: (9 + 11 + 14 + 10 + 16) ÷ 5 = 60 ÷ 5 = 12 ✓

📋 Example with a Table

Many GED problems present data in a table. The strategy is identical — just read the known values from the table first.

Day	Hours Worked
Monday	7
Tuesday	9
Wednesday	6
Thursday	8
Friday	?

The mean is 7.4 hours per day. What is Friday's value?

Solution

Step 1 — Add known values: 7 + 9 + 6 + 8 = 30

Step 2 — Required total: 5 × 7.4 = 37

Step 3 — Missing value: 37 − 30 = 7

Friday = 7 hours

🎯 Multiple Choice Strategy — Work Backwards

On multiple-choice GED questions, you have a powerful shortcut: plug each answer choice into the missing spot and check whether the mean comes out right.

Work-backwards strategy: Take each answer choice, add it to the known values, divide by the total number of values, and see which one gives you the correct mean. This can often be faster than solving from scratch — especially if the answer choices are close together.

GED test writers often expect students to use strategies like this. There is no rule that says you must solve it the "traditional" way. Use whatever gets you to the right answer efficiently.

⚠️ Common Mistakes

❌ Dividing Instead of Multiplying

Students divide the mean by the number of values. But the first operation here is multiplication: Total = Mean × Count. Division comes at the end when you verify.

❌ Forgetting to Count the Missing Value

If the problem has 5 values total, you always use 5 — even though one is missing. The missing number is still one of the values. Using 4 instead of 5 gives the wrong required total.

❌ Subtracting Backwards

Always subtract: Required Total − Known Total. The required total is always bigger. Subtracting the wrong way gives a negative answer.

❌ Dividing by Only the Visible Numbers

If 5 numbers have a mean, you divide by 5 — not 4 just because only 4 are visible. The count is always the total number of values including the missing one.

✏️ Practice Questions

Bank 1 — Skill Building

Guided reasoning — builds the concept step by step

You've answered 5 questions. Keep going or check your score.

Bank 2 — GED-Level Practice

Real-world problems with tables and practical contexts

You've answered 5 questions. Keep going or check your score.

Up Next in Stage 5

Finding Slope

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