💡 8th Grade Math (Algebra I): Mean, Median, Mode, and Range Practice Questions
1
Solved Example
Easy Level
Let's find the mean, median, mode, and range for the following set of test scores:
85
92
78
85
90
💡 Mean: The average of the numbers. Median: The middle number when the data is ordered. Mode: The number that appears most often. Range: The difference between the highest and lowest numbers.
Solution & Explanation
Here's how to calculate each measure:
Mean:
First, sum all the scores: \( 85 + 92 + 78 + 85 + 90 = 430 \).
Then, divide the sum by the number of scores (which is 5): \( \frac{430}{5} = 86 \).
The mean score is 86.
Median:
First, order the scores from least to greatest: \( 78, 85, 85, 90, 92 \).
The middle number is the third score, which is 85.
Mode:
Look for the number that repeats the most. The score 85 appears twice, more than any other score.
Range:
Find the highest score (92) and the lowest score (78).
Subtract the lowest from the highest: \( 92 - 78 = 14 \).
The range is 14.
2
Solved Example
Easy Level
Calculate the mean, median, mode, and range for this list of temperatures recorded over a week:
22°C
25°C
23°C
25°C
26°C
24°C
25°C
Solution & Explanation
Let's break it down:
Mean:
Sum of temperatures: \( 22 + 25 + 23 + 25 + 26 + 24 + 25 = 170 \).
Number of temperatures: 7.
Mean: \( \frac{170}{7} \approx 24.29 \)°C. The mean temperature is approximately 24.29°C.
Median:
Ordered temperatures: \( 22, 23, 24, 25, 25, 25, 26 \).
The middle number (4th) is 25°C.
Mode:
The temperature that occurs most frequently is 25°C (it appears 3 times).
Range:
Highest temperature: 26°C.
Lowest temperature: 22°C.
Range: \( 26 - 22 = 4 \)°C. The range is 4°C.
3
Solved Example
Medium Level
A basketball player scored the following points in their last 5 games:
18
24
15
24
20
What is the median number of points scored? What is the mode?
Solution & Explanation
Let's find the median and mode:
Median:
First, arrange the scores in ascending order: \( 15, 18, 20, 24, 24 \).
Since there are 5 scores, the median is the middle score, which is the 3rd score. The median is 20 points.
Mode:
The score that appears most often is 24 points, as it occurs twice.
4
Solved Example
Medium Level
Consider the following set of numbers:
5, 12, 8, 5, 15, 10, 5, 12
Find the mean and the range of this dataset.
Solution & Explanation
Here's how to find the mean and range:
Mean:
Sum of the numbers: \( 5 + 12 + 8 + 5 + 15 + 10 + 5 + 12 = 72 \).
There are 8 numbers in the set.
Mean: \( \frac{72}{8} = 9 \). The mean is 9.
Range:
The highest number is 15.
The lowest number is 5.
Range: \( 15 - 5 = 10 \). The range is 10.
5
Solved Example
Medium Level
Sarah's scores on her math quizzes are: 88, 95, 76, 95, and 82. Her teacher says that if she gets a 90 on her next quiz, her mean score will increase by 1 point.
Is the teacher correct? Explain your reasoning. 🤔
Solution & Explanation
Let's check the teacher's statement:
Current Mean:
Sum of current scores: \( 88 + 95 + 76 + 95 + 82 = 436 \).
Number of scores: 5.
Current mean: \( \frac{436}{5} = 87.2 \).
New Mean with a 90:
If Sarah scores a 90, the new sum will be \( 436 + 90 = 526 \).
The new number of scores will be 6.
New mean: \( \frac{526}{6} \approx 87.67 \).
Comparison:
The increase in the mean is \( 87.67 - 87.2 = 0.47 \).
The teacher stated the mean would increase by 1 point. Since \( 0.47 \neq 1 \), the teacher is not correct.
6
Solved Example
Medium Level
A dataset has a median of 15. If you add the number 25 to the dataset, how will the median change? What if you add the number 5 instead? 🧐
Solution & Explanation
Let's analyze how adding numbers affects the median:
Scenario 1: Adding 25
The original median is 15. This means that when the data is ordered, 15 is the middle value. Adding a number larger than the current median (25 > 15) will push the middle value to the right if the dataset has an odd number of elements, or it might stay the same if the dataset has an even number of elements and 15 was already one of the two middle numbers. However, without knowing the original dataset, we can infer that adding a larger number will likely keep the median at 15 or potentially shift it slightly higher, but it won't decrease. If the original set was \( \{10, 15, 20\} \), adding 25 gives \( \{10, 15, 20, 25\} \), and the median becomes \( \frac{15+20}{2} = 17.5 \). If the original set was \( \{10, 15, 20, 22\} \), adding 25 gives \( \{10, 15, 20, 22, 25\} \), and the median remains 20. The key is that 25 is greater than or equal to the original median, so it won't pull the median down.
Scenario 2: Adding 5
Adding a number smaller than the current median (5 < 15) will likely pull the median down or keep it the same. If the original set was \( \{10, 15, 20\} \), adding 5 gives \( \{5, 10, 15, 20\} \), and the median becomes \( \frac{10+15}{2} = 12.5 \). If the original set was \( \{10, 15, 15, 20\} \), adding 5 gives \( \{5, 10, 15, 15, 20\} \), and the median remains 15. The number 5 is less than or equal to the original median, so it won't pull the median up.
Key takeaway: Adding a value larger than the median tends to increase or keep the median the same, while adding a value smaller than the median tends to decrease or keep the median the same. The exact change depends on the original dataset's size and values.
7
Solved Example
Real World Example
A small bakery wants to know the typical price of their cupcakes. They recorded the prices of 7 different cupcakes:
3.50
4.00
3.75
4.00
3.25
4.00
3.50
What is the mode price of a cupcake? What is the mean price? 🧁
Solution & Explanation
Let's find the typical cupcake prices:
Mode:
The price that appears most often is 4.00, as it occurs 3 times. This indicates it's the most common price.
Mean:
Sum of prices: \( \3.50 + \4.00 + \3.75 + \4.00 + \3.25 + \4.00 + \3.50 = \26.00 \).
Number of cupcakes: 7.
Mean: \( \frac{\26.00}{7} \approx \3.71 \). The mean price is approximately 3.71.
👉 The mode (4.00) gives a clear idea of the most frequent price, while the mean (3.71) provides an average price, considering all prices.
8
Solved Example
Real World Example
A group of friends is trying to decide on a movie to watch. They each suggest a movie and vote on it. The number of votes each movie received is:
Movie A: 5 votes
Movie B: 3 votes
Movie C: 5 votes
Movie D: 2 votes
Movie E: 5 votes
Movie F: 4 votes
Which movie is the most popular based on the mode? What is the range of votes received by the movies? 🎬
Solution & Explanation
Let's determine the most popular movie and the spread of votes:
Mode:
The number of votes that appears most often is 5 votes. Movies A, C, and E all received 5 votes, making them the most popular choices according to the mode.
Range:
The highest number of votes is 5.
The lowest number of votes is 2.
Range: \( 5 - 2 = 3 \). The range of votes is 3.
📌 The mode helps identify the most frequent outcome (most popular movies), while the range shows the difference between the most and least popular movies.
8th Grade Math (Algebra I): Mean, Median, Mode, and Range Practice Questions
Example 1:
Let's find the mean, median, mode, and range for the following set of test scores:
85
92
78
85
90
💡 Mean: The average of the numbers. Median: The middle number when the data is ordered. Mode: The number that appears most often. Range: The difference between the highest and lowest numbers.
Solution:
Here's how to calculate each measure:
Mean:
First, sum all the scores: \( 85 + 92 + 78 + 85 + 90 = 430 \).
Then, divide the sum by the number of scores (which is 5): \( \frac{430}{5} = 86 \).
The mean score is 86.
Median:
First, order the scores from least to greatest: \( 78, 85, 85, 90, 92 \).
The middle number is the third score, which is 85.
Mode:
Look for the number that repeats the most. The score 85 appears twice, more than any other score.
Range:
Find the highest score (92) and the lowest score (78).
Subtract the lowest from the highest: \( 92 - 78 = 14 \).
The range is 14.
Example 2:
Calculate the mean, median, mode, and range for this list of temperatures recorded over a week:
22°C
25°C
23°C
25°C
26°C
24°C
25°C
Solution:
Let's break it down:
Mean:
Sum of temperatures: \( 22 + 25 + 23 + 25 + 26 + 24 + 25 = 170 \).
Number of temperatures: 7.
Mean: \( \frac{170}{7} \approx 24.29 \)°C. The mean temperature is approximately 24.29°C.
Median:
Ordered temperatures: \( 22, 23, 24, 25, 25, 25, 26 \).
The middle number (4th) is 25°C.
Mode:
The temperature that occurs most frequently is 25°C (it appears 3 times).
Range:
Highest temperature: 26°C.
Lowest temperature: 22°C.
Range: \( 26 - 22 = 4 \)°C. The range is 4°C.
Example 3:
A basketball player scored the following points in their last 5 games:
18
24
15
24
20
What is the median number of points scored? What is the mode?
Solution:
Let's find the median and mode:
Median:
First, arrange the scores in ascending order: \( 15, 18, 20, 24, 24 \).
Since there are 5 scores, the median is the middle score, which is the 3rd score. The median is 20 points.
Mode:
The score that appears most often is 24 points, as it occurs twice.
Example 4:
Consider the following set of numbers:
5, 12, 8, 5, 15, 10, 5, 12
Find the mean and the range of this dataset.
Solution:
Here's how to find the mean and range:
Mean:
Sum of the numbers: \( 5 + 12 + 8 + 5 + 15 + 10 + 5 + 12 = 72 \).
There are 8 numbers in the set.
Mean: \( \frac{72}{8} = 9 \). The mean is 9.
Range:
The highest number is 15.
The lowest number is 5.
Range: \( 15 - 5 = 10 \). The range is 10.
Example 5:
Sarah's scores on her math quizzes are: 88, 95, 76, 95, and 82. Her teacher says that if she gets a 90 on her next quiz, her mean score will increase by 1 point.
Is the teacher correct? Explain your reasoning. 🤔
Solution:
Let's check the teacher's statement:
Current Mean:
Sum of current scores: \( 88 + 95 + 76 + 95 + 82 = 436 \).
Number of scores: 5.
Current mean: \( \frac{436}{5} = 87.2 \).
New Mean with a 90:
If Sarah scores a 90, the new sum will be \( 436 + 90 = 526 \).
The new number of scores will be 6.
New mean: \( \frac{526}{6} \approx 87.67 \).
Comparison:
The increase in the mean is \( 87.67 - 87.2 = 0.47 \).
The teacher stated the mean would increase by 1 point. Since \( 0.47 \neq 1 \), the teacher is not correct.
Example 6:
A dataset has a median of 15. If you add the number 25 to the dataset, how will the median change? What if you add the number 5 instead? 🧐
Solution:
Let's analyze how adding numbers affects the median:
Scenario 1: Adding 25
The original median is 15. This means that when the data is ordered, 15 is the middle value. Adding a number larger than the current median (25 > 15) will push the middle value to the right if the dataset has an odd number of elements, or it might stay the same if the dataset has an even number of elements and 15 was already one of the two middle numbers. However, without knowing the original dataset, we can infer that adding a larger number will likely keep the median at 15 or potentially shift it slightly higher, but it won't decrease. If the original set was \( \{10, 15, 20\} \), adding 25 gives \( \{10, 15, 20, 25\} \), and the median becomes \( \frac{15+20}{2} = 17.5 \). If the original set was \( \{10, 15, 20, 22\} \), adding 25 gives \( \{10, 15, 20, 22, 25\} \), and the median remains 20. The key is that 25 is greater than or equal to the original median, so it won't pull the median down.
Scenario 2: Adding 5
Adding a number smaller than the current median (5 < 15) will likely pull the median down or keep it the same. If the original set was \( \{10, 15, 20\} \), adding 5 gives \( \{5, 10, 15, 20\} \), and the median becomes \( \frac{10+15}{2} = 12.5 \). If the original set was \( \{10, 15, 15, 20\} \), adding 5 gives \( \{5, 10, 15, 15, 20\} \), and the median remains 15. The number 5 is less than or equal to the original median, so it won't pull the median up.
Key takeaway: Adding a value larger than the median tends to increase or keep the median the same, while adding a value smaller than the median tends to decrease or keep the median the same. The exact change depends on the original dataset's size and values.
Example 7:
A small bakery wants to know the typical price of their cupcakes. They recorded the prices of 7 different cupcakes:
3.50
4.00
3.75
4.00
3.25
4.00
3.50
What is the mode price of a cupcake? What is the mean price? 🧁
Solution:
Let's find the typical cupcake prices:
Mode:
The price that appears most often is 4.00, as it occurs 3 times. This indicates it's the most common price.
Mean:
Sum of prices: \( \3.50 + \4.00 + \3.75 + \4.00 + \3.25 + \4.00 + \3.50 = \26.00 \).
Number of cupcakes: 7.
Mean: \( \frac{\26.00}{7} \approx \3.71 \). The mean price is approximately 3.71.
👉 The mode (4.00) gives a clear idea of the most frequent price, while the mean (3.71) provides an average price, considering all prices.
Example 8:
A group of friends is trying to decide on a movie to watch. They each suggest a movie and vote on it. The number of votes each movie received is:
Movie A: 5 votes
Movie B: 3 votes
Movie C: 5 votes
Movie D: 2 votes
Movie E: 5 votes
Movie F: 4 votes
Which movie is the most popular based on the mode? What is the range of votes received by the movies? 🎬
Solution:
Let's determine the most popular movie and the spread of votes:
Mode:
The number of votes that appears most often is 5 votes. Movies A, C, and E all received 5 votes, making them the most popular choices according to the mode.
Range:
The highest number of votes is 5.
The lowest number of votes is 2.
Range: \( 5 - 2 = 3 \). The range of votes is 3.
📌 The mode helps identify the most frequent outcome (most popular movies), while the range shows the difference between the most and least popular movies.