Graph Totals and Differences
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ISEE Lower Level: Mathematics Achievement › Graph Totals and Differences
A scatter plot shows the relationship between hours studied and test scores for 30 students. The data reveals that 8 students studied 0-2 hours and scored an average of 65 points, 12 students studied 3-5 hours and scored an average of 78 points, and 10 students studied 6+ hours and scored an average of 89 points. If we calculate the total points earned by all students in each study group, how many more total points did the 3-5 hour group earn compared to the 0-2 hour group?
156 more total points were earned by the 0-2 hour study group than the 3-5 hour group
416 more total points were earned by the 3-5 hour study group than the 0-2 hour group
416 more total points were earned by the 0-2 hour study group than the 3-5 hour group
156 more total points were earned by the 3-5 hour study group than the 0-2 hour group
Explanation
When you encounter scatter plot problems involving grouped data, you need to calculate total values by multiplying the number of students in each group by their average score, then compare the results.
Let's find the total points for each study group. For the 0-2 hour group: 8 students × 65 average points = 520 total points. For the 3-5 hour group: 12 students × 78 average points = 936 total points. To find how many more points the 3-5 hour group earned, subtract: 936 - 520 = 416 more points.
Looking at the wrong answers: Choice A gives the correct direction (3-5 hour group earned more) but uses 156 instead of 416 - this might come from incorrectly calculating the difference between average scores (78 - 65 = 13) and then multiplying by 12 students. Choice B has the right number (416) but claims the 0-2 hour group earned more, which reverses the comparison since 520 < 936. Choice D combines both errors - wrong direction and wrong calculation, suggesting the 0-2 hour group earned 156 more points.
The correct answer is C: the 3-5 hour group earned 416 more total points than the 0-2 hour group.
Study tip: In grouped data problems, always multiply the group size by the average to get totals before making comparisons. Don't just compare the averages themselves - the group sizes matter significantly in determining total outcomes.
A histogram displays test scores for two classes. Class A had 8 students score between 90-100, 12 students score between 80-89, 15 students score between 70-79, and 5 students score below 70. Class B had 11 students score between 90-100, 9 students score between 80-89, 18 students score between 70-79, and 2 students score below 70. What is the total number of students who scored 80 or above across both classes combined?
80 students scored 80 or above when combining both classes together
50 students scored 80 or above when combining both classes together
40 students scored 80 or above when combining both classes together
60 students scored 80 or above when combining both classes together
Explanation
Students scoring 80 or above include those in the 80-89 and 90-100 ranges. Class A: 8 + 12 = 20 students scored 80 or above. Class B: 11 + 9 = 20 students scored 80 or above. Combined total: 20 + 20 = 40 students. Choice A incorrectly includes students from the 70-79 range. Choice C gives the total number of all students in both classes. Choice D uses an incorrect partial calculation.
A school cafeteria tracked the number of meals sold each day for two weeks. In the first week, they sold 245, 268, 291, 256, and 223 meals from Monday through Friday. In the second week, they sold 312, 289, 267, 294, and 258 meals from Monday through Friday. What is the difference between the total number of meals sold in the second week compared to the first week?
127 more meals in the second week than the first week
137 more meals in the first week than the second week
137 more meals in the second week than the first week
127 more meals in the first week than the second week
Explanation
First week total: 245 + 268 + 291 + 256 + 223 = 1,283 meals. Second week total: 312 + 289 + 267 + 294 + 258 = 1,420 meals. Difference: 1,420 - 1,283 = 137 meals. Since the second week had more meals, the answer is 137 more meals in the second week. Choice B incorrectly reverses which week had more. Choices C and D use an incorrect calculation of 127 instead of 137.
A pictograph shows how many cupcakes were sold at a bake sale. Each cupcake symbol represents 5 cupcakes. Chocolate shows 9 symbols, vanilla shows 7 symbols, and strawberry shows 4 symbols. How many more chocolate and strawberry cupcakes were sold than vanilla cupcakes?
6 cupcakes
25 cupcakes
10 cupcakes
30 cupcakes
Explanation
First, find the total number of chocolate and strawberry cupcakes. This is (9 + 4) symbols = 13 symbols. Convert this to cupcakes: 13 symbols × 5 cupcakes/symbol = 65 cupcakes. Next, find the number of vanilla cupcakes: 7 symbols × 5 cupcakes/symbol = 35 cupcakes. Finally, find the difference: 65 - 35 = 30 cupcakes.