ISEE Middle Level Quiz: Mean Median And Mode
20 questions · exam conditions
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Mean Median And ModeQuestion 1 of 20

A list of 9 numbers has a median of 15. Six of the numbers are 8, 11, 12, 20, 22, and 25. Which of the following could be the other three numbers?

13, 14, 16
16, 17, 18
15, 16, 17
14, 15, 16
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ISEE Middle Level Quiz

ISEE Middle Level Quiz: Mean Median And Mode

Practice Mean Median And Mode in ISEE Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Mean Median And Mode, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A list of 9 numbers has a median of 15. Six of the numbers are 8, 11, 12, 20, 22, and 25. Which of the following could be the other three numbers?

  1. 13, 14, 16
  2. 16, 17, 18
  3. 15, 16, 17
  4. 14, 15, 16 (correct answer)
Explanation: When you encounter a median problem with missing values, remember that the median is the middle number when all values are arranged in order. With 9 numbers, the median will be the 5th number in the ordered list. Since the median is 15, you know that when all 9 numbers are arranged from least to greatest, the 5th position must contain 15. Let's work with the given numbers: 8, 11, 12, 20, 22, 25. To find which three numbers work, arrange the known values and see where the missing numbers must fall. You need the 5th number overall to equal 15. Looking at the given numbers, 12 is less than 15, and 20 is greater than 15. This means you need some numbers between 12 and 20 to make 15 the median. For choice D (14, 15, 16): Arranging all numbers gives you 8, 11, 12, 14, 15, 16, 20, 22, 25. The 5th number is indeed 15, confirming this is correct. Choice A (13, 14, 16) creates the sequence 8, 11, 12, 13, 14, 16, 20, 22, 25, making 14 the median. Choice B (16, 17, 18) gives 8, 11, 12, 16, 17, 18, 20, 22, 25, making 17 the median. Choice C (15, 16, 17) produces 8, 11, 12, 15, 16, 17, 20, 22, 25, making 16 the median. Study tip: Always arrange all numbers in order and count to the middle position. With median problems involving missing values, work systematically by testing where the missing numbers fit in the ordered sequence.

Question 2

The mode of a list of 8 integers is 25. The median is 22. The mean is 20. Which of the following numbers must be in the list?

  1. 20
  2. 22
  3. 25 (correct answer)
  4. 28
Explanation: The mode is the number that appears most frequently. Since the mode is 25, the number 25 must appear in the list more times than any other number. Therefore, 25 must be in the list. The mean is the average and does not have to be one of the numbers in the list. The median of 8 integers is the average of the 4th and 5th integers when sorted; while their average is 22, neither 22 nor numbers that average to it are guaranteed to be in the set (e.g., the 4th and 5th could be 21 and 23). However, the mode, by definition, must be a value present in the data set.

Question 3

A class tracks 11 cafeteria apples sold daily: 18, 20, 20, 21, 22, 22, 22, 23, 24, 25, 26. What is the mean of the data set in the passage?

  1. 21
  2. 22 (correct answer)
  3. 23
  4. 24
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 11 daily apples sold: 18, 20, 20, 21, 22, 22, 22, 23, 24, 25, 26, which requires calculating the mean. The correct answer is choice B because it accurately reflects the mean calculated as 243 divided by 11 equals 22.0909, but wait, sum is 18+20+20+21+22+22+22+23+24+25+26=243, 243/11=22.0909, but choices are integers, perhaps rounded to 22. But marked is B 22. Good.

Question 4

Coach Rivera tracks 10 game points to set practice goals: 8, 10, 12, 12, 14, 16, 16, 18, 20, 22. What is the mean of the data set in the passage?

  1. 14.8 (correct answer)
  2. 15.0
  3. 14.0
  4. 16.0
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 10 game points: 8, 10, 12, 12, 14, 16, 16, 18, 20, 22, which requires calculating the mean. The correct answer is choice A because it accurately reflects the mean calculated as 148 divided by 10 equals 14.8. This shows understanding of statistical measures. Choice B is incorrect because it represents 15.0, possibly from rounding prematurely or misadding. This error occurs when students forget to divide by the total number of items accurately. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 5

The basketball team scores 11 games: 9, 11, 12, 12, 13, 14, 14, 14, 15, 16, 18. Which number appears most frequently, indicating the mode?

  1. 12
  2. 13
  3. 14 (correct answer)
  4. 16
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 11 basketball game scores: 9, 11, 12, 12, 13, 14, 14, 14, 15, 16, 18, which requires calculating the mode. The correct answer is choice C because it accurately reflects the mode calculated as 14, appearing three times. This shows understanding of statistical measures. Choice A is incorrect because it represents 12, which appears only twice. This error occurs when students miscount repetitions. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 6

A coach lists 11 free-throw makes to plan drills: 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10. What does the median tell you about the data distribution?

  1. Half the values are at or below 7. (correct answer)
  2. 7 is the most common value.
  3. 7 is the total of all values.
  4. All values are higher than 7.
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 11 free-throw makes: 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, which requires interpreting the median. The correct answer is choice A because it accurately reflects that half the values are at or below 7, the median. This shows understanding of statistical measures. Choice B is incorrect because 7 is the mode, not what the median indicates. This error occurs when students confuse median with mode. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 7

The weekly allowances of five siblings are $10, $12, $15, $18, and $45. If the sibling with the highest allowance has it reduced to $20, which of the following describes the change in the mean and median?

  1. The mean decreases and the median stays the same. (correct answer)
  2. The mean stays the same and the median decreases.
  3. Both the mean and the median decrease.
  4. The mean decreases and the median increases.
Explanation: Original set: {$10, $12, $15, $18, $45}. The median is the middle value, 15.Themeanis(15. The mean is (10+12+12+15+18+18+45)/5 = $100/5 = 20. New set: {10, $12, $15, $18, $20}. The median is still the middle value, 15.Thenewmeanis(15. The new mean is (10+12+12+15+18+18+20)/5 = $75/5 = $15. The mean decreased from $20 to $15, while the median stayed the same at $15.

Question 8

In a class of 25 students, 12 students are 11 years old, 8 students are 12 years old, and 5 students are 13 years old. What is the mean age of the students in the class, to the nearest tenth of a year?

  1. 11.7 (correct answer)
  2. 12.0
  3. 12.3
  4. 11.5
Explanation: To find the mean age, we calculate a weighted average. The sum of all the ages is (12 students × 11 years) + (8 students × 12 years) + (5 students × 13 years) = 132 + 96 + 65 = 293 years. The total number of students is 25. The mean age is the total sum of ages divided by the number of students: 293 / 25 = 11.72. Rounded to the nearest tenth, the mean age is 11.7 years.

Question 9

During a five-day charity drive, a school raised $150, $200, $150, $250, and $180. The school's goal was to have a mean fundraising amount of $200 per day. How much more money did they need to raise on the fifth day to meet their goal exactly?

  1. $20
  2. $50
  3. $70 (correct answer)
  4. $90
Explanation: To have a mean of $200 over five days, the total amount raised must be 5 × $200 = $1000. The amount actually raised over the five days is $150 + $200 + $150 + $250 + $180 = $930. The school was short of its goal by $1000 - $930 = $70. To meet the goal, this $70 shortfall needed to be raised on one of the days. The question asks how much more was needed on the fifth day. The amount needed on the fifth day to meet the goal is the target total minus the sum of the first four days: 1000−(1000 - (150 + $200 + $150 + $250) = $1000 - $750 = $250. They raised $180 on the fifth day, so they needed to raise $250 - $180 = $70 more on that day.

Question 10

The number of goals scored by a soccer team in its last 11 matches are: 2, 3, 0, 1, 1, 2, 4, 1, 2, 3, 1. What is the median number of goals scored?

  1. 1
  2. 1.5
  3. 2 (correct answer)
  4. 2.5
Explanation: To find the median, first, we must arrange the number of goals in ascending order: 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4. There are 11 matches, which is an odd number. The median is the middle value, which is the (11 + 1) / 2 = 6th value in the sorted list. Counting to the 6th value, we find it is 2. Thus, the median number of goals scored is 2.

Question 11

The mean weight of 8 boxes is 12 pounds. If two boxes, each weighing 12 pounds, are added, what is the new mean weight?

  1. 10 pounds
  2. 12 pounds (correct answer)
  3. 14 pounds
  4. 24 pounds
Explanation: The total weight of the original 8 boxes is 8 × 12 = 96 pounds. Two new boxes are added, each weighing 12 pounds. The total weight of the added boxes is 2 × 12 = 24 pounds. The new total weight is 96 + 24 = 120 pounds. The new number of boxes is 8 + 2 = 10. The new mean weight is 120 / 10 = 12 pounds. Alternatively, since the weight of the added boxes is equal to the original mean, the mean will not change.

Question 12

The prices of five different laptops are $500, $750, $600, $1200, and $600. If a sixth laptop priced at $2500 is added to the group, how does the median price change?

  1. It increases by $50.
  2. It increases by $75. (correct answer)
  3. It increases by $150.
  4. It stays the same.
Explanation: First, find the median of the original five prices. Sorted prices: $500, $600, $600, $750, $1200. The median is the middle value, which is $600. Now, add the sixth laptop priced at $2500. The new sorted list of six prices is: $500, $600, $600, $750, $1200, $2500. With an even number of items, the median is the average of the two middle values (the 3rd and 4th). The middle values are $600 and 750.Thenewmedianis(750. The new median is (600 + $750) / 2 = $1350 / 2 = $675. The median changed from $600 to $675, which is an increase of $75.

Question 13

Students measure 10 plant heights (cm) for science: 12, 13, 14, 14, 15, 16, 16, 17, 18, 20. Based on the data, what is the median value?

  1. 14
  2. 15
  3. 15.5 (correct answer)
  4. 16
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 10 plant heights: 12, 13, 14, 14, 15, 16, 16, 17, 18, 20, which requires calculating the median. The correct answer is choice C because it accurately reflects the median calculated as the average of 15 and 16, which is 15.5. This shows understanding of statistical measures. Choice A is incorrect because it represents 14, ignoring the average for even count. This error occurs when students pick one middle number instead of averaging. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 14

Mr. Chen lists 10 science test scores to adjust lessons: 62, 68, 70, 74, 76, 78, 82, 84, 90, 96. Based on the data, what is the median value?

  1. 76
  2. 77 (correct answer)
  3. 78
  4. 74
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 10 science test scores: 62, 68, 70, 74, 76, 78, 82, 84, 90, 96, which requires calculating the median. The correct answer is choice B because it accurately reflects the median calculated as the average of 76 and 78, which is 77. This shows understanding of statistical measures. Choice A is incorrect because it represents 76, ignoring the need to average the two middle numbers. This error occurs when students forget to average for even-numbered data sets. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 15

In a class survey, 10 students choose books read this month: 1, 2, 2, 3, 3, 3, 4, 4, 5, 6. What is the mean of the data set in the passage?

  1. 3.0
  2. 3.3 (correct answer)
  3. 3.6
  4. 4.0
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 10 books read: 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, which requires calculating the mean. The correct answer is choice B because it accurately reflects the mean calculated as 33 divided by 10 equals 3.3. This shows understanding of statistical measures. Choice A is incorrect because it represents 3.0, possibly from rounding down incorrectly. This error occurs when students miscalculate the sum. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 16

Coach Lee tracks 12 practice lap times (minutes): 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 12. Which number appears most frequently, indicating the mode?

  1. 7
  2. 8 (correct answer)
  3. 9
  4. 10
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 12 practice lap times: 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 12, which requires calculating the mode. The correct answer is choice B because it accurately reflects the mode calculated as 8, appearing three times. This shows understanding of statistical measures. Choice A is incorrect because it represents 7, which appears only twice. This error occurs when students confuse mode with other measures. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 17

A basketball coach records 12 points per game: 10, 12, 12, 13, 14, 14, 14, 15, 16, 16, 18, 20. If a new data point is added, how does it affect the mean?

  1. Adding 14 keeps the mean the same. (correct answer)
  2. Adding 10 increases the mean.
  3. Adding 20 decreases the mean.
  4. Adding 12 keeps the mean the same.
Explanation: This question tests middle school mathematics achievement: finding mean, median, or mode from a data set. The mean is calculated by adding all values and dividing by the total number of data points, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this passage, the data set involves 12 basketball points: 10, 12, 12, 13, 14, 14, 14, 15, 16, 16, 18, 20, which requires determining the effect on the mean when adding a new point. The correct answer is choice A because adding 14 keeps the mean the same, as the original mean is 14 (168/12), and adding 14 makes it (182/13) ≈14. This shows understanding of statistical measures. Choice B is incorrect because adding 10 would decrease the mean, not increase it. This error occurs when students miscalculate the original mean. To help students: Encourage practice with ordering data sets for median, ensure careful calculation for mean, and recognize patterns for mode. Watch for: students confusing terms, skipping steps in calculations, and ignoring data points.

Question 18

The mean of five test scores is 87. Four of the scores are 85, 92, 88, and 80. What is the fifth test score?

  1. 86
  2. 87
  3. 88
  4. 90 (correct answer)
Explanation: The mean is the sum of the scores divided by the number of scores. If the mean of five scores is 87, their sum must be 5 × 87 = 435. The sum of the four known scores is 85 + 92 + 88 + 80 = 345. To find the fifth score, subtract the sum of the four scores from the total sum: 435 - 345 = 90.

Question 19

The mean score of 10 boys on a quiz is 78. The mean score of 20 girls on the same quiz is 84. What is the mean score for all 30 students?

  1. 80
  2. 81
  3. 82 (correct answer)
  4. 83
Explanation: This requires finding the weighted average. The total score for the boys is 10 × 78 = 780. The total score for the girls is 20 × 84 = 1680. The total score for all students is 780 + 1680 = 2460. The total number of students is 10 + 20 = 30. The combined mean is the total score divided by the total number of students: 2460 / 30 = 82.

Question 20

For the set of numbers {7, 2, 8, 2, 6}, which of the following statements is true?

  1. The mean is greater than the median.
  2. The mode is equal to the mean.
  3. The mode is greater than the median.
  4. The median is greater than the mean. (correct answer)
Explanation: When you encounter a question comparing mean, median, and mode, you need to calculate each measure of central tendency systematically and then compare them. Let's work with the set {7, 2, 8, 2, 6}. First, find the mode (the most frequently occurring value). The number 2 appears twice while all others appear once, so the mode is 2. Next, calculate the median by arranging the numbers in order: {2, 2, 6, 7, 8}. The median is the middle value, which is 6. For the mean, add all values and divide by the count: 7+2+8+2+65=255=5\frac{7 + 2 + 8 + 2 + 6}{5} = \frac{25}{5} = 5 Now compare: mode = 2, median = 6, mean = 5. Since 6 > 5, the median is greater than the mean. Choice A is wrong because the mean (5) is actually less than the median (6), not greater. Choice B is incorrect because the mode (2) and mean (5) are completely different values. Choice C is false because the mode (2) is actually smaller than the median (6), not greater. Choice D correctly states that the median is greater than the mean (6 > 5). Study tip: Always organize your work when comparing measures of central tendency. Calculate mode first (easiest to spot), then arrange the data in order to find the median, and finally compute the mean. Write down all three values before comparing them to avoid careless errors.