ASVAB Study Guide
Statistics and Probability · Lesson 2 of 3

Calculating a Missing Value Given the Mean

Key rules and formulas, worked examples and 3 practice problems with step-by-step solutions.

Finding a Missing Score

Calculating an unknown value when the desired average is known.

Average = Total number of points / Number of graded papers (or Target Sum = Target Mean × Total Items)

Multiply the target mean by the total number of items to get the required sum.

Example

A student needs an average of 80 on 3 tests. Their first two scores are 75 and 82. What must they score on the third test?

Show solution

Step 1: Find the total points needed for 3 tests: $$80 \times 3 = 240$$

Step 2: Add the scores of the tests already completed: $$75 + 82 = 157$$

Step 3: Subtract the current sum from the required total points: $$240 - 157 = 83$$

Practice problems

  1. Problem 1

    Sam wants his bowling average over 4 games to be 150. His first three game scores are 140, 160, and 130. What score does he need in his fourth game?

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    Answer: 170

    Step 1: Calculate the total points needed for 4 games: $$150 \times 4 = 600$$

    Step 2: Add the three completed game scores: $$140 + 160 + 130 = 430$$

    Step 3: Subtract the current points from the total points needed: $$600 - 430 = 170$$

  2. Problem 2

    A salesperson wants to average 20 sales per day across 5 days. From Monday to Thursday, they made 18, 22, 15, and 21 sales. How many sales must they achieve on Friday?

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    Answer: 24

    Step 1: Calculate the required total sales for 5 days: $$20 \times 5 = 100$$

    Step 2: Add the sales completed from Monday to Thursday: $$18 + 22 + 15 + 21 = 76$$

    Step 3: Subtract the current sum from the required total: $$100 - 76 = 24$$

  3. Problem 3

    The average weight of 3 packages is 12 pounds. Two of the packages weigh 10 pounds and 15 pounds. What is the weight of the third package?

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    Answer: 11 pounds

    Step 1: Calculate the required total weight for all 3 packages: $$12 \times 3 = 36$$ pounds

    Step 2: Add the weights of the two known packages: $$10 + 15 = 25$$ pounds

    Step 3: Subtract the known weight from the total required weight: $$36 - 25 = 11$$ pounds

Remember

Don't forget to include the missing item in the total count when multiplying the target mean.