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Quizzes > High School Quizzes > Mathematics

Finding the Average Practice Quiz

Master averages with interactive practice questions

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting Ace the Average Quiz for middle school students.

What is the average of 3, 5, and 7?
5
6
7
8
The average is calculated by adding the numbers (3 + 5 + 7 = 15) and then dividing by the count of numbers (3). This yields an average of 5.
If you have the numbers 10, 20, and 30, what is their average?
20
25
15
30
Adding the numbers gives 10 + 20 + 30 = 60, and then dividing by 3 gives 20. That is the correct method for calculating an average.
How do you calculate the average of a set of numbers?
Divide the sum of the numbers by how many numbers there are
Multiply all the numbers together
Subtract the smallest number from the largest
Add the first and last number only
The average is found by adding all the numbers and then dividing the total by the number of values present. This method is the standard formula for calculating an average.
What is the average of 4, 4, and 4?
4
12
0
8
Since all the numbers are identical, their sum is 12 and, when divided by 3, the average remains 4. This reflects the property that the average of identical numbers is the number itself.
Calculate the average of two numbers: 8 and 12.
10
8
12
9
The sum of 8 and 12 is 20, and dividing 20 by 2 gives an average of 10. This is a direct application of the average formula.
Find the average of the numbers: 5, 8, 10, and 7.
7.5
7
8
8.5
Adding the numbers gives 5 + 8 + 10 + 7 = 30, and dividing by 4 results in an average of 7.5. This question tests the basic averaging of a small dataset.
What is the average of 12, 15, and 18?
15
16
14
17
The sum of the numbers is 12 + 15 + 18 = 45. Dividing 45 by 3 gives an average of 15, which is the correct answer.
A student scored 80, 90, 70, and 85 on four tests. What is the average score?
81.25
80
85
82.5
The total score is 80 + 90 + 70 + 85 = 325. Dividing 325 by 4 gives an average of 81.25. The question reinforces averaging with non-rounded outcomes.
Find the average of these five numbers: 4, 6, 8, 10, and 12.
8
7
9
10
The sum of the numbers is 4 + 6 + 8 + 10 + 12 = 40. Dividing 40 by 5 gives an average of 8, which is the correct calculation.
Which method correctly calculates the average of a set of numbers?
Divide the sum of all numbers by the count of numbers
Multiply the numbers and then take the square root
Subtract the smallest number from the largest
Add only the first and last numbers and divide by 2
The correct formula for the average is to sum all the values and then divide by the quantity of values. This option correctly states that method.
If the average of 10, 15, and x is 12, what is the value of x?
11
12
13
10
Using the average formula: (10 + 15 + x)/3 = 12 leads to 25 + x = 36. Solving for x gives x = 11.
If the average of five test scores is 78 and four scores are 80, 76, 75, and 82, what is the fifth score?
77
78
80
75
The total needed for an average of 78 over 5 tests is 390. Since the sum of the four given scores is 313, the missing score must be 390 - 313 = 77.
A basketball player scores 12, 9, 15, and 14 points in four games. What is his average score?
12.5
12
13
11.5
The sum of the scores is 12 + 9 + 15 + 14 = 50. Dividing 50 by 4 gives an average of 12.5, which is the correct result.
A teacher recorded the number of books read by students as 2, 3, 5, 7, and 11. What is the average number of books read?
5.6
6
5
7
The total number of books is 2 + 3 + 5 + 7 + 11 = 28. Dividing 28 by 5 gives an average of 5.6. This demonstrates averaging with a non-integer result.
Calculate the average of 6 numbers: 4, 5, 6, 7, 8, and 9.
6.5
6
7
5.5
Adding the numbers gives 4 + 5 + 6 + 7 + 8 + 9 = 39, and dividing 39 by 6 results in an average of 6.5. The solution applies the standard average calculation.
The average of 8 numbers is 20. When two numbers are removed, the new average becomes 18. What is the sum of the two removed numbers?
52
36
40
30
Originally, the total sum is 8 x 20 = 160. After removing two numbers, the remaining 6 numbers sum to 6 x 18 = 108. The sum of the removed numbers is 160 - 108 = 52.
The average of four consecutive even numbers is 17. What is the largest number in the set?
20
18
22
24
Let the numbers be x, x+2, x+4, and x+6. Their average is x+3, which equals 17. Solving for x gives 14, making the largest number 14+6 = 20.
A group of 10 students has an average test score of 85. If one student's score is mistakenly recorded as 75 instead of 95, what is the corrected average score?
87
85
88
90
The original total score is 10 x 85 = 850. Replacing 75 with 95 increases the total by 20, giving a new sum of 870. Dividing by 10 results in a corrected average of 87.
In a math competition, the scores of five participants are 12, 15, x, 18, and 20. If the average score is 16, what is the value of x?
15
16
14
17
The total required for an average of 16 over 5 participants is 16 x 5 = 80. The sum of the known scores is 12 + 15 + 18 + 20 = 65, so x must be 80 - 65 = 15.
The average of a set of numbers is 25. If every number in the set is increased by 5, what is the new average?
30
25
35
20
When each number is increased by 5, the overall sum increases by 5 times the number of elements. Thus, the average increases by 5, resulting in a new average of 25 + 5 = 30.
0
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Study Outcomes

  1. Calculate the average of given data sets accurately.
  2. Analyze numerical information to identify central trends.
  3. Interpret word problems involving averages effectively.
  4. Apply average calculations to improve exam strategies.
  5. Evaluate how changes in data affect overall averages.

Finding the Average Worksheets Cheat Sheet

  1. Understanding the Mean - The mean, or average, is found by adding all numbers in a set and then dividing by how many numbers you have. It's like sharing slices of pizza equally among friends so everyone gets the same-sized piece. This measure gives you the "central" value but watch out - extremely high or low numbers can skew it! Mean, Mode, Median & Range Guide
  2. Mastering the Median - The median is the middle value when your data is sorted from smallest to largest. If there's an even number of items, you simply find the mean of the two center numbers. This makes the median a great way to see what's typical without letting outliers rule the day! Mean, Mode, Median & Range Guide
  3. Identifying the Mode - The mode is the value that pops up most often in your set - think of it as the "pop star" of your data. You can have one mode, multiple modes, or none at all if every number is unique. This is super handy when you want to know the most common outcome, like the bestselling smartphone color! Mean, Mode, Median & Range Guide
  4. Calculating the Range - The range shows how spread out your numbers are by subtracting the smallest value from the largest. It's the simplest way to measure variability - like finding the gap between the shortest and tallest players on a basketball team. Just remember, it doesn't tell you about anything happening in between! Mean, Mode, Median & Range Guide
  5. Applying Averages to Real-Life Data - Averages help us make sense of huge piles of information, from class scores to daily temperatures. By summarizing data into a single number, you get a quick snapshot of overall trends. This makes it easier to spot improvements, set goals, or just brag about your stellar test performance! Mean, Mode, Median & Range Guide
  6. Comparing Mean and Median - While the mean considers every value, the median only cares about the middle point, making it more resilient to outliers. If your data has extreme highs or lows (like a few billionaires in a town), the median can give a fairer picture of what's "normal." Use both to get the full story! BBC Bitesize: Mean vs Median
  7. Recognizing the Importance of Mode - The mode reveals the most frequent value, which is perfect for spotting popular choices - like the favorite ice-cream flavor in class. It's straightforward and doesn't get fiddled by extreme values. When you want to know what the majority prefers, the mode is your go-to! BBC Bitesize: Mode Explained
  8. Understanding the Significance of Range - Range gives a quick sense of how varied your data can be, highlighting the gap between the smallest and largest values. It's key in quality control, like checking if product sizes stay within acceptable limits. Remember, it won't tell you about the distribution in the middle, so pair it with other stats! BBC Bitesize: Range & Variability
  9. Calculating Averages from Frequency Tables - When data is in a frequency table, multiply each value by its frequency, add up those products, then divide by the total frequency to find the mean. It's like weighting your pizza slices by their popularity. This method gives you a quick average when raw data points aren't listed individually! BBC Bitesize: Working with Frequency Tables
  10. Exploring Grouped Data - With grouped data, approximate the mean by using the midpoint of each class interval multiplied by its frequency, then divide by the total frequency. You can also estimate the mode by finding the modal class with the highest frequency. These tricks help you summarize large datasets when exact values are hidden in ranges! BBC Bitesize: Grouped Data Techniques
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