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.

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.

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.

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.

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.

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.

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.

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.

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.

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.