ISEE Middle Level Mathematics Achievement Quiz: Mean Median And Mode

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 Mathematics Achievement.

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.

Question 1

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 2

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 3

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 4

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. The new median is ($600 + $750) / 2 =$1350 / 2 = $675. The median changed from$600 to $675, which is an increase of$75.

Question 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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: $\frac{7 + 2 + 8 + 2 + 6}{5} = \frac{25}{5} = 5$ 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.

Question 17

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. The mean is ($10+$12+$15+$18+$45)/5 =$100/5 = 20. New set: {10, $12,$15, $18,$20}. The median is still the middle value, $15. The new mean is ($10+$12+$15+$18+$20)/5 = $75/5 =$15. The mean decreased from $20 to$15, while the median stayed the same at $15.

Question 18

1. 88
2. 88.5
3. 89 (correct answer)
4. 90

Explanation: To find the median, first order the scores from least to greatest: 85, 88, 88, 90, 92, 95. Since there is an even number of scores (six), the median is the average of the two middle scores. The two middle scores are the 3rd and 4th values, which are 88 and 90. The average is (88 + 90) / 2 = 178 / 2 = 89.

Question 19

1. (5m - 53) (correct answer)
2. (m - 53)
3. (5m + 53)
4. ((m+53)/5)

Explanation: The mean of a set of numbers is their sum divided by the count. So, the sum of the five numbers is (5 \times m = 5m). The sum of the four known numbers is 8 + 11 + 14 + 20 = 53. Let the fifth number be (x). Then, (53 + x = 5m). Solving for (x), we get (x = 5m - 53).

Question 20

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.