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Quizzes > Mathematics

Average Test: Practice Mean Calculations

Quick, free average quiz to sharpen mean calculations. Instant results.

Editorial: Review CompletedCreated By: Jack FoleyUpdated Aug 25, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration of numbers symbols and clock on sky blue background representing free average calculation quiz

This quiz helps you practice calculating the average (mean) of number sets with speed and accuracy. Build fluency with quick questions, then explore broader skills in our statistics quiz with answers and target key concepts in the ap statistics chapter 4 quiz.

What is the arithmetic mean of the numbers 5, 10, and 15?
12.5
15
5
10
The arithmetic mean is calculated by adding all the values and dividing by their count. Here, adding 5, 10, and 15 gives 30 and dividing by 3 yields 10. That makes 10 the correct answer.
Calculate the mean of the numbers 8, 12, and 20.
13.33
14
12
11.67
The mean is the sum of the numbers divided by their count. Adding 8, 12, and 20 gives 40, and dividing by 3 yields approximately 13.33. Therefore, 13.33 is the correct average.
Find the average of the four identical values: 4, 4, 4, and 4.
5
3
4
4.5
When all values are identical, the mean is that same value. Since each number is 4, their average remains 4. No calculation beyond recognizing identical values is needed.
If the average of three numbers is 10 and two of the numbers are 8 and 12, what is the third number?
10
12
8
9
The total sum needed for an average of 10 with three numbers is 30. Two known numbers sum to 8 + 12 = 20. Subtracting 20 from 30 gives 10, the missing number.
The average of five test scores is 80. Four of the scores are 75, 85, 90, and 70. What is the fifth score?
90
85
80
75
The total sum for an average of 80 across five tests is 400. The sum of the four given scores is 75 + 85 + 90 + 70 = 320. Subtracting 320 from 400 gives 80, the fifth score.
A midterm counts for 40% of a grade and the final counts for 60%. If the midterm score is 85 and the final score is 95, what is the weighted average?
92
93
91
90
Weighted average = 0.4×85 + 0.6×95 = 34 + 57 = 91. This method accounts for differing weights by multiplying each score by its respective percentage.
The average temperature from Monday to Friday is 68°F. Given Monday through Thursday were 65, 70, 72, and 66°F, what was Friday's temperature?
68
66
69
67
Total needed for a 68°F average over five days is 340°F. The first four days sum to 65 + 70 + 72 + 66 = 273°F. Subtracting gives 340 - 273 = 67°F for Friday.
In a class of 30 students, the average age is 15. A new student age 17 joins the class. What is the new average age?
15
15.5
15.06
14.9
Original total age = 30 × 15 = 450. Adding a 17-year-old gives 467. Dividing by 31 students yields approximately 15.06.
If a car travels to a destination at 60 mph and returns over the same distance at 40 mph, what is its average speed for the entire trip?
55 mph
50 mph
48 mph
52 mph
Average speed over equal distances uses the harmonic mean: 2/(1/60 + 1/40) = 48 mph. This accounts for the fact that time spent at each speed differs.
What is the geometric mean of 3 and 12?
6
7
5
4
The geometric mean of two numbers is the square root of their product: ?(3×12) = ?36 = 6. It is used to find the central tendency of rates and ratios.
A portfolio consists of 30% in Stock A with an 8% return and 70% in Stock B with a 12% return. What is the portfolio's overall return?
9.6%
10.8%
10%
11%
Weighted return = 0.3×8% + 0.7×12% = 2.4% + 8.4% = 10.8%. This method applies each return by its allocation weight.
If the mean of n numbers is m and a new number x is added, resulting in a new mean of M, which expression gives x?
M(n+1) - n m
M n - m(n+1)
(n m + M)/(n+1)
m(n+1) - n M
Original sum = n×m. After adding x, total = n m + x and count = n+1. Setting (n m + x)/(n+1) = M and solving gives x = M(n+1) - n m.
The harmonic mean of three numbers 3, 4, and x is 4. What is the value of x?
4
3
12
6
The harmonic mean H of a,b,c is 3/(1/a + 1/b + 1/c). Setting 3/(1/3 + 1/4 + 1/x) = 4 leads to 1/3 + 1/4 + 1/x = 3/4. Solving for 1/x gives 1/6, so x = 6.
0
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Study Outcomes

  1. Calculate Arithmetic Averages -

    Quickly compute arithmetic means using standard formulas in our calculate averages quiz.

  2. Apply Averages to Real-World Problems -

    Solve practical scenarios - like test scores and data analysis - by finding averages accurately in our find average quiz.

  3. Leverage the Quiz Average Calculator -

    Use the built-in quiz average calculator tool to verify answers and access instant scoring feedback.

  4. Identify Common Calculation Pitfalls -

    Recognize frequent mistakes in average calculations and learn strategies to avoid them.

  5. Enhance Speed and Accuracy -

    Develop efficient techniques to calculate averages faster while maintaining precision in your results.

Cheat Sheet

  1. Arithmetic Mean Formula -

    The arithmetic mean is the sum of all data points divided by the total count, expressed as x̄ = (∑xi)/n, a cornerstone concept in any average calculation quiz. According to MIT OpenCourseWare, mastering this formula is critical for rapid scoring on an average test. Try the mnemonic "sum then split" to remember to add before you divide.

  2. Weighted Average Fundamentals -

    Weighted averages account for varying importance by multiplying each value by its weight and dividing by the total weight: x̄w = (∑wi·xi)/(∑wi). The American Statistical Association highlights this method when combining grades or rates, like GPA calculations. Practice with a quiz average calculator to see how different weights shift your result.

  3. Median vs. Mode Distinctions -

    While the mean can be skewed by outliers, the median (middle value) and mode (most frequent) often give clearer insight into data distributions, per Khan Academy. In a find average quiz, choose median for skewed sets and mode for categorical data. Remember: "median sits in the middle, mode opens the door" to recall which measure applies.

  4. Grouping Data with Frequency Tables -

    For large datasets, use frequency tables and midpoints to estimate the mean: x̄ ≈ (∑fi·mi)/N, where fi is frequency and mi is class midpoint, an approach taught at university statistics courses. This technique simplifies average calculation quizzes when raw data are grouped. Always verify class widths are consistent to ensure accuracy.

  5. Quick Estimation and Mental Math Tricks -

    Develop estimation skills by rounding values to closest tens or fives before averaging, reducing calculation time on a calculate averages quiz. Research from math education journals shows mental estimation boosts speed without sacrificing much accuracy. Use paired rounding - round low values up and highs down - to balance errors and sharpen test performance.

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