Analyzing Graphs and Figures

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Pre-Algebra › Analyzing Graphs and Figures

Questions 1 - 10
1

Pie_graph

Four candidates ran for mayor of Jackson City; the above circle graph shows the share of the vote that each won.

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above graph, which of the following is the outcome of the vote?

Mills and Jones will face each other in a runoff.

Mills won the election outright.

Jones won the election outright.

Mills and King will face each other in a runoff.

Jones and King will face each other in a runoff.

Explanation

By comparing the sizes of the sectors, it can be seen that Mills won the largest share of the vote - but not at least one half of it - and Jones won the second-largest share. Therefore, they will face each other in a runoff.

2

What percentage of books are NOT science fiction?

Pie chart

Explanation

A pie chart contains portions that total to 100%. To find the percentage of books that are NOTscience fiction, we subtract the percentage of science fiction from 100%.

Pie chart

The percentage of books that are sicence fiction is 17%. So,

Therefore, 83% of the books are NOTscience fiction.

3

Using the following bar graph, what is the total number of books borrowed by Jessica and Emma?

Graph

Explanation

When reading a bar graph, each bar contains different information. Look at the following bar graph.

Graph

The names of each student are displayed at the bottom. The number of books borrowed is displayed at the left. Each bar represents the number of books borrowed by a specific student.

We are asked to find the total number of books borrowed by Jessica and Emma. If we locate Jessica's name on the bottom, we can see the value of the bar is 5. This means Jessica borrowed 5 books. If we locate Emma's name on the bottom, we can see the value of the bar is 4. Now, finding the total number of books borrowed by Jessica and Emma, we simply add.

So the total number of books borrowed by Jessica and Emma is 9.

4

What is the midpoint of the following sets of coordinates.

Explanation

The midpoint formula is:

Given our points are we can plug them into the midpoint formula and get the following.

Simplifing the we find the coordinate of the midpoint.

5

Find the mean and median of the following set of numbers.

Mean = 6

Median = 6

Mean = 66

Median = 3

Mean = 11

Median = 2

Mean = 8

Median = 10

Mean = 9

Median = 8

Explanation

Average or Mean is the total divided by the number of items.

Total equals 66, divided by the 11 numbers equals 6.

The Median is the middle number when put in order from least to greatest.

Five numbers on the left of 6 and five numbers on the right of 6. Six is in the middle when in order from least to greatest.

Answer is 6.

Mean = 6

Median = 6

6

Pie_graph

Five candidates ran for mayor of Madison City; the above circle graph shows the share of the vote that each won. Which of the following would be the most reasonable estimate of the percent of the vote Lyle won?

%

%

%

%

%

Explanation

The sector representing Lyle is roughly one-tenth to one-eighth of the circle - in other words, 10-12 % of it. This is the approximate percent of the vote won by Lyle.

7

If a line crosses through the points and , where does it cross the -axis?

Explanation

Don't forget, when graphing points on a graph go left or right first then go up or down.

(2,8) and (3,9) has a slope of 1.

The slope is found using the formula,

where

and

Rise of 1 and a Run of 1.

Other coordinates are

The line will cross the y-axis at .

8

Histogram

Refer to the above bar graph.

What percent of the students achieved a score above 400?

Explanation

30 students achieved a score of 401-500; 40 students achieved a score of 501-600; 16 achieved a score of 601-700; 10 achieved a score of 701-800. Add these:

The number of students who took the test is the sum of the students who finished in the six ranges:

The question is now to find out what percent 96 is of 120, which can be calculated as follows:

9

Find the slope of the line between the points and .

Explanation

Recall the slope formula:

Plug in the two given points:

The slope of the line is .

10

Histogram

Refer to the above graph. Clark, a sixth grader at Polk, outscored 100 of the students who took the test. What could his score have been?

Explanation

students achieved scores between 200 and 600, and Clark outscored all of them.

students achieved scores between 200 and 700; Clark did not outscore all of them.

Therefore, his score fell in the range from 601 to 700, making 635 the only plausible choice of the five.

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