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Quizzes > High School Quizzes > Mathematics

Mean, Mode, Median & Range Practice Quiz

Sharpen stats skills with worksheet answer key

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Paper art depicting trivia quiz for middle school math students focusing on mean, mode, median concepts.

What is the mean of the numbers 4, 8, 12?
6
8
10
12
The mean is calculated by adding all the numbers and then dividing by the number of values. In this case, (4 + 8 + 12) / 3 equals 8, which is the correct answer.
Which term describes the average value calculated by adding numbers and dividing by the total count?
Mean
Mode
Median
Range
The process of adding all numbers and dividing by the count defines the mean. This is the standard method for calculating the arithmetic average.
What is the mode of the set: {2, 3, 3, 5, 7}?
2
3
5
7
The mode is the number that appears most frequently in a set. In this set, 3 appears twice while the other numbers appear only once.
If the median of a set is 6, what does it represent?
The arithmetic average
The middle value in an ordered set
The most frequent number
The range of the set
The median represents the middle value when all numbers are arranged in order. It divides the data into two halves, with half the values below and half above it.
How is the range of a data set determined?
Largest number minus smallest number
Sum of all numbers divided by the count
The middle value after ordering
The number that appears most frequently
The range measures the spread of data by subtracting the smallest value from the largest. This gives a simple indication of how spread out the numbers are.
What is the median of the list: 5, 1, 9, 3, 7?
3
5
7
9
First, arrange the numbers in order: 1, 3, 5, 7, 9. The median is the middle value of the ordered list, which is 5.
Find the mode in the data set: 4, 4, 4, 8, 8, 9, 9, 9, 9, 10.
4
8
9
10
The mode is determined by identifying which number appears most frequently. Here, 9 appears four times, more than any other number in the set.
Calculate the range for the numbers: 16, 22, 9, 30, 18.
12
21
30
9
The range is found by subtracting the smallest number from the largest number. Here, 30 - 9 equals 21, which is the correct range.
What is the mean of the following set: 10, 15, 20, 25, 30?
15
20
25
30
To find the mean, add all the numbers and divide by the total count. With a sum of 100 divided by 5, the mean comes out to 20.
If a data set has one distinct mode, what does this indicate?
All numbers are equally frequent
There is a tie for frequent numbers
One number appears most frequently
The mean is the same as the mode
A distinct mode means one number occurs more often than any other in the set. This characteristic pinpoints the most common value in the dataset.
Which measure of central tendency is most affected by outliers?
Median
Mode
Mean
Range
Outliers have a strong influence on the mean because they alter the total sum used in its calculation. The median and mode generally remain less affected by extreme values.
Which measure of central tendency best represents the center in a skewed distribution?
Median
Range
Mode
Mean
In skewed distributions, the median is more reliable because it is not distorted by extreme values. It accurately reflects the central position of the data.
For the set {1, 2, 2, 3, 4}, what is the median?
1
2
3
4
Arranging the set in order gives 1, 2, 2, 3, 4. With the middle value being the third number, the median is 2.
In a set with an even number of data points, how is the median determined?
The larger of the two middle numbers
The smaller of the two middle numbers
The average of the two middle numbers
The difference between the two middle numbers
When a dataset has an even number of values, there is no single middle number. Instead, the median is found by averaging the two central numbers.
What is the mode of the set: 1, 2, 3, 4, 5?
1
3
There is no mode
5
Since each number in the set appears exactly once, no number occurs more frequently than another. Therefore, the set is considered to have no mode.
A teacher records the test scores: 55, 70, 70, 80, 85, 90, 100. What is the median score?
70
80
85
90
After ordering the scores, the middle value in the list of seven numbers is the fourth one. This makes 80 the median score.
Given a data set where adding an outlier increases the mean by 5 but leaves the median unchanged, what can be deduced about the added value?
The outlier is close to the median
The outlier is much higher or lower than the existing values
The dataset had no variation before
The mode also increases
Outliers primarily affect the mean by altering the overall sum. Since the median remains unchanged, the added value must be significantly different from the central cluster of data.
For the data set 3, 8, 5, 12, 7, 5, 9, 5, what is the mode and why?
3
5
7
9
The mode is the number that appears most frequently in the dataset. In this case, the number 5 appears three times, more than any other number, making it the mode.
If the median of a data set with an even number of values is not given, how can it be determined?
By selecting the lowest value
By taking the average of the two middle numbers
By choosing the higher of the two middle numbers
By calculating the mean first
An even number of values means there are two numbers in the middle. The median is found by averaging these two central numbers, which provides an accurate middle value.
If two data sets have identical mean, median, and mode but different ranges, what does this indicate?
They have identical variability
One set has a larger spread of values
Their central tendencies are inaccurately calculated
They must be from the same distribution
While mean, median, and mode describe central tendency, the range measures data spread. A different range indicates that one dataset has more variability or a wider spread of values than the other.
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Study Outcomes

  1. Calculate mean, mode, and median from a variety of data sets.
  2. Explain the differences between measures of central tendency.
  3. Analyze data sets to identify the most representative value.
  4. Interpret results to assess strengths and identify areas for improvement.
  5. Apply central tendency concepts to solve real-world mathematical problems.

Mean Mode Median & Range Answer Key Cheat Sheet

  1. Understanding the Mean - The mean (or average) is found by adding all the values in your set and dividing by how many numbers you have. It gives you a quick snapshot of the "center" of your data. Perfect for spotting whether your scores are generally high or low! Learn more
  2. Calculating the Median - The median is the middle value once you've lined your numbers up from smallest to largest. If there's an even number of values, you simply average the two middle ones - easy peasy! It's a great way to dodge extreme outliers in your set. Learn more
  3. Identifying the Mode - The mode is the number that shows up most often in your data. You might have one mode, two modes (bimodal), or even no mode if every number is unique. Handy for spotting trends or the most common result in a survey! Learn more
  4. Determining the Range - Range measures how spread out your numbers are by subtracting the smallest from the largest. A big range means your data is all over the place; a small range means it's pretty tight-knit. Super useful for quickly gauging variability! Learn more
  5. Handling Data Sets with No Mode - If no number repeats, your set doesn't have a mode. That's totally fine and actually tells you every value is unique. It's a quick flag for diversity in your data points. Learn more
  6. Calculating Mean with Decimals - Decimals join the party just like whole numbers: add them all up, then divide by the count. Be sure to line up those decimal points neatly for spot‑on precision. It's a tiny extra step that keeps your average nice and accurate! Learn more
  7. Finding Median in Even-Sized Data Sets - When you have an even number of data points, average the two in the middle to find your median. This trick keeps things fair and square, even when there's no single middle value. It's your secret weapon against imbalance! Learn more
  8. Understanding Bimodal and Multimodal Sets - If two values tie for most frequent, your data is bimodal; more than two and it's multimodal. This tells you there are multiple "popular" numbers in your set. Great for uncovering complex patterns at a glance! Learn more
  9. Interpreting the Range - A larger range signals big swings between your smallest and largest values, while a tiny range shows consistency. Use it to get a feel for how crazy - or calm - your data is behaving. It's like a quick weather report for your numbers!
  10. Practice with Real-World Data - Applying these concepts to things you care about - like game scores, temperatures, or snack ratings - locks in your learning. Grab some data, try your calculations, and watch the "aha!" moments roll in. Real practice is the ultimate study hack! Learn more
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