This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (2, 3, 4, 2, 5, 3, 2, 6, 4, 3, 2, 5), you can find the mode by counting frequencies: 2 appears four times, 3 appears three times, 4 appears twice, 5 appears twice, and 6 appears once. Choice C is correct because 2 appears four times, more frequently than any other value in the data set. Choice B is incorrect because 5 only appears twice, which is less frequent than both 2 and 3 - this error may occur when students confuse mode with other measures or don't count systematically. To help students: Create a frequency distribution table listing each unique value and its count. The mode is always the value with the highest frequency, not necessarily the highest value.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (12, 8, 15, 12, 10, 18, 9, 12, 14, 8), you can find the mode by counting how many times each number appears: 8 appears twice, 12 appears three times, and all other numbers appear once. Choice B is correct because 12 is the most frequently occurring value, appearing three times in the data set. Choice A is incorrect because 8 only appears twice, which is less frequent than 12. To help students: Create a frequency table listing each unique value and its count, then identify which value has the highest frequency. Always double-check your counting to avoid errors.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (7, 11, 9, 16, 11, 13, 10, 8, 14, 11), you can find the range by first identifying the highest value (16) and the lowest value (7), then calculating 16 - 7 = 9. Choice A is correct because it accurately reflects the calculation of the range as the difference between the maximum and minimum values. Choice B is incorrect because 23 represents adding the highest and lowest values (16 + 7) rather than subtracting them, a common conceptual error. To help students: Always arrange data from smallest to largest first, clearly identify the maximum and minimum values, then subtract minimum from maximum. Remind students that range measures spread, not sum.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (58, 61, 63, 60, 65, 62, 59, 66, 64, 61, 60, 67, 62, 60), you can find the range by identifying the highest value (67) and the lowest value (58), then calculating 67 - 58 = 9. Choice A is correct because it accurately reflects the calculation of the range as the difference between the maximum and minimum values. Choice B is incorrect because 125 represents adding all the highest and lowest values or some other calculation error, showing fundamental misunderstanding of the range concept. To help students: Practice identifying maximum and minimum values by scanning through data systematically. Remember that range is always maximum minus minimum, never addition or multiplication.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (10, 6, 12, 9, 10, 15, 8, 10, 7, 14, 11), you must first order the 11 values: 6, 7, 8, 9, 10, 10, 10, 11, 12, 14, 15, then find the middle value, which is the 6th value: 10. Choice A is correct because when the data is properly ordered, the median (middle value) is 10. Choice C is incorrect because 11 is the 8th value in the ordered list, not the middle value - this error occurs when students count from the wrong end or miscalculate the middle position. To help students: For odd-numbered data sets, use the formula (n+1)/2 to find the position of the median, where n is the number of values. Always order data first and double-check your counting.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (55, 62, 70, 68, 74, 81, 77, 90, 85, 62, 79, 88, 73, 66, 62), you can find the range by identifying the highest value (90) and the lowest value (55), then calculating 90 - 55 = 35. Choice A is correct because it accurately reflects the calculation of the range as the difference between the maximum and minimum values. Choice C is incorrect because 145 represents adding the highest and lowest values (90 + 55) rather than subtracting them, demonstrating confusion about the range formula. To help students: Remember that range measures the spread of data, calculated as maximum minus minimum. Create a habit of circling or highlighting the highest and lowest values before calculating.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (70, 72, 68, 71, 69, 70, 73, 74, 70, 67, 75), first order the 11 values: 67, 68, 69, 70, 70, 70, 71, 72, 73, 74, 75, then find the middle (6th) value: 70. Choice A is correct because with 11 values, the median is the 6th value in the ordered list, which is 70. Choice B is incorrect because 71 is the 7th value, not the 6th - this error occurs when students count the middle position incorrectly or fail to order the data properly first. To help students: For odd-numbered data sets, use (n+1)/2 to find the median position. Always order data from least to greatest before finding the median.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (62, 65, 60, 63, 66, 62, 64, 67, 61, 62, 65, 68, 62, 64), you can find the mode by counting frequencies: 60 appears once, 61 once, 62 appears four times, 63 once, 64 appears twice, 65 appears twice, 66 once, 67 once, and 68 once. Choice B is correct because 62 appears four times, more frequently than any other temperature value. Choice A is incorrect because 65 only appears twice, which is less frequent than 62 - this error occurs when students don't systematically count all occurrences. To help students: Use tally marks or a frequency table to track each value's occurrences systematically. Always recount to verify, especially with larger data sets.

This question tests high school mathematics achievement skills: determining range, median, and mode from a data set. The range is the difference between the highest and lowest values, the median is the middle value when data is ordered, and the mode is the most frequently occurring number. In this data set (64, 71, 85, 90, 77, 82, 68, 75, 88, 92, 71, 79, 83, 71, 86), first order the 15 values: 64, 68, 71, 71, 71, 75, 77, 79, 82, 83, 85, 86, 88, 90, 92, then find the middle (8th) value: 79. Choice A is correct because with 15 values, the median is the 8th value in the ordered list, which is 79. Choice D is incorrect because 77 is the 7th value, not the 8th - this error occurs when students miscount the position or start counting from zero instead of one. To help students: For odd-numbered data sets, the median position is (n+1)/2 = (15+1)/2 = 8. Always verify by counting from both ends to ensure you've found the true middle.