Table and Graph Interpretation
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ISEE Middle Level: Mathematics Achievement › Table and Graph Interpretation
A report on city parks provides the following data on the number of trees in four parks: Park A has 150 trees, Park B has 200, Park C has 120, and Park D has 180. What is the median number of trees in these four parks?
150
165
170
180
Explanation
To find the median of a data set, first arrange the numbers in order: 120, 150, 180, 200. Since there is an even number of data points (four), the median is the average of the two middle numbers. The two middle numbers are 150 and 180. Their average is (150 + 180) / 2 = 330 / 2 = 165. Distractor C is the mean (650/4 = 162.5, close but not quite). A and D are the middle two values themselves.
A table displays the amount of rainfall, in inches, for two cities over a three-month period. City X: May 3.2, June 2.8, July 4.0. City Y: May 2.5, June 3.5, July 3.0. For the entire three-month period, what was the difference in total rainfall between the two cities?
1.2 inches
0.2 inches
1.0 inch
0.7 inches
Explanation
First, calculate the total rainfall for City X: 3.2 + 2.8 + 4.0 = 10.0 inches. Next, calculate the total rainfall for City Y: 2.5 + 3.5 + 3.0 = 9.0 inches. The difference between their total rainfall is 10.0 - 9.0 = 1.0 inch. Distractors are based on differences in single months (e.g., May difference is 0.7).
A survey of 50 students asked them to rate a new school lunch on a scale of 1 to 5. The results were recorded in a frequency table: 5 students gave a rating of 1, 10 students gave a rating of 2, 15 students gave a rating of 3, 12 students gave a rating of 4, and 8 students gave a rating of 5. What was the average rating for the new school lunch?
2.9
3.0
3.2
3.5
Explanation
To find the average rating, we calculate a weighted average. Multiply each rating by the number of students who gave that rating, sum these products, and then divide by the total number of students. The calculation is: (51 + 102 + 153 + 124 + 8*5) / 50 = (5 + 20 + 45 + 48 + 40) / 50 = 158 / 50 = 3.16. The closest answer is 3.2.
A library tracks the number of books checked out each day. Monday: 150, Tuesday: 180, Wednesday: 210, Thursday: 160, Friday: 240, Saturday: 260. What is the average number of books checked out per day from Monday to Saturday?
185
200
205
215
Explanation
To find the average, sum the number of books for all six days and divide by 6. Total books = 150 + 180 + 210 + 160 + 240 + 260 = 1200. Average = 1200 ÷ 6 = 200 books per day. Distractors represent common calculation errors or using only certain days.
A data table shows the number of minutes two students, Maya and Liam, spent on homework each day for a week. Maya's times were: 45, 60, 50, 70, 55. Liam's times were: 60, 50, 55, 40, 70. What is the difference between the medians of their homework times?
10 minutes
15 minutes
5 minutes
0 minutes
Explanation
To find the median, first order the data for each student. Maya's times in order are: 45, 50, 55, 60, 70. The median (middle value) is 55. Liam's times in order are: 40, 50, 55, 60, 70. The median is 55. The difference between their medians is 55 - 55 = 0 minutes.
A table shows the results of a survey on students' favorite sports. Out of 120 students surveyed, 40% chose basketball, 25% chose soccer, 15% chose baseball, and the rest chose swimming. How many more students chose basketball than swimming?
20
24
30
48
Explanation
First, find the number of students who chose basketball: 40% of 120 is 0.40 * 120 = 48. Next, find the percentage who chose swimming. The total percentage is 100%. So, 100% - 40% - 25% - 15% = 20% chose swimming. The number of students who chose swimming is 20% of 120, which is 0.20 * 120 = 24. The difference is 48 - 24 = 24. Distractor A is the percentage for swimming. D is the number of students who chose basketball. C is the number who chose soccer.
A table compares the populations of Town A and Town B over three decades. In 1990, Town A had 5,200 people and Town B had 6,000. In 2000, Town A had 5,800 and Town B had 6,700. In 2010, Town A had 6,600 and Town B had 7,400. In which decade was the absolute population growth of Town A greater than that of Town B?
1990 to 2000 only
2000 to 2010 only
In neither decade
In both decades
Explanation
Calculate the population growth for each town in each decade. From 1990 to 2000: Town A grew by 5,800 - 5,200 = 600 people. Town B grew by 6,700 - 6,000 = 700 people. Here, Town B's growth was greater. From 2000 to 2010: Town A grew by 6,600 - 5,800 = 800 people. Town B grew by 7,400 - 6,700 = 700 people. Here, Town A's growth was greater. Therefore, Town A's growth was greater than Town B's only in the decade from 2000 to 2010.
A survey of 80 middle school students asked whether they preferred to read fiction or non-fiction books. A two-way table shows the results: 26 of the 48 boys preferred fiction. In total, 50 students preferred fiction. How many girls preferred non-fiction?
8
10
22
30
Explanation
First, organize the data. Total students = 80. Total boys = 48, so Total girls = 80 - 48 = 32. Total fiction = 50, so Total non-fiction = 80 - 50 = 30. We know 26 boys preferred fiction. Since 50 students in total preferred fiction, the number of girls who preferred fiction is 50 - 26 = 24. Since there are 32 girls in total, and 24 preferred fiction, then 32 - 24 = 8 girls preferred non-fiction.
A table shows the scores for three students on a test with a maximum score of 120. Aria scored 82, Ben scored 78, and Cara scored 92. What was the group's average score as a percentage of the maximum possible score?
65%
70%
84%
88%
Explanation
First, calculate the average score of the three students: (82 + 78 + 92) / 3 = 252 / 3 = 84. This is the average score. The question asks for this average score as a percentage of the maximum possible score, which is 120. To find this percentage, divide the average score by the maximum score and multiply by 100: (84 / 120) * 100%. This simplifies to (7 / 10) * 100% = 0.7 * 100% = 70%. Distractor C is the average score itself.
The results of a class fundraiser are shown in a table. The four grades in a school raised the following amounts: 6th grade raised $450, 7th grade raised $600, 8th grade raised $500, and 9th grade raised $450. The total amount raised was what fraction of the 7th grade's total?
1/4
3/10
2/3
10/3
Explanation
First, calculate the total amount raised by all grades: $450 + $600 + $500 + $450 = $2000. The question asks for the ratio of the total amount to the 7th grade's amount. This is $2000 / $600. Simplifying this fraction gives 20/6, which further simplifies to 10/3. A common mistake is to calculate the 7th grade's contribution as a fraction of the total (600/2000 = 3/10), which is distractor C.