### All HiSET: Math Resources

## Example Questions

### Example Question #1 : Summarize And Interpret Data Presented Verbally, Tabularly, And Graphically

Researchers performed a survey of the populations of several small islands. The data is represented by the following histogram.

What percentage of islands surveyed had a population of less than 140?

**Possible Answers:**

35%

0%

30%

65%

55%

**Correct answer:**

65%

On the horizontal axis of a histogram, you have labels representing ranges of values. For example, the label "140–159" represents the range of islands with populations between 140 and 159.

The question asks for the percent of islands with populations under 140. The ranges that are smaller than 140 are the "120–139" range and the "100–119" range. Match the bars of each with the percents on the vertical (*y*) axis. The percents corresponding to these ranges are 35% and 30%, respectively.

Adding both of these percents yields the answer, 65%.

### Example Question #1 : Data Analysis, Probability, And Statistics

The revenue of a small company over 10 years is portrayed by the following line graph.

Which of the following statements can best be made about the data?

**Possible Answers:**

The company's revenue increased from 1991 to 1993.

The company had the highest revenue in the year 1994.

The company's revenue generally decreased from 1994 to 1996.

The revenue in the 10 years was generally decreasing each year.

The revenue in the 10 years was generally increasing each year.

**Correct answer:**

The company's revenue generally decreased from 1994 to 1996.

The question asks you to identify a trend that best fits the data.

Over 10 years, the revenue of the company decreases and increases with no clear overall pattern or trend, so the answers claiming that there is a general increase or decrease are incorrect.

While the revenue was at a high point ($65,000) in the year 1994, it was not the highest point in the 10 years. The highest point was in 1998, with a revenue of $77,000.

While the revenue did increase from 1991 to 1992, it decreased by even more from 1991 to 1993. Therefore, from 1991 to 1993, there was actually a net decrease in revenue, not a net increase.

The correct answer is: "The company's revenue generally decreased from 1994 to 1996." Notice the data points matching the years 1994, 1995, and 1996 are linked by a line that has a downward slope. This indicates a general decrease in revenue.

### Example Question #1 : Summarize And Interpret Data Presented Verbally, Tabularly, And Graphically

An individual's income over 10 years is represented by the following line chart.

Approximate individual's highest annual income from 1994 to 1998.

**Possible Answers:**

$500

$210,000

$460,000

$500,000

$460

**Correct answer:**

$460,000

Notice that the question narrows the time period you are examining to 1994–1998. While there are years with higher incomes than in this time period (namely, 1992 and 1999), we can only consider the years from 1994 to 1998.

The highest point within this period is in the year 1998. Matching this data point with the values on the y-axis (the income values), you will see that this data point lies between $400,000 and $500,000. Looking more closely, you can even say that it is above halfway between the values, so it appears to be greater than $450,000.

Thus, the value that approximates the income in 1998 is $460,000.

Be careful to take into account the units on each axis. The y-axis measures income in thousands of dollars, so the answer is $460,000 and not $460.

### Example Question #1 : Data Analysis, Probability, And Statistics

Which of these data sets would be best represented using a line graph?

**Possible Answers:**

The average amount spent on groceries per week by families of different income levels.

The distribution of ages of employees at a software company

The decrease in weight of a dieting adult male over the last 12 months

The distribution of various weekly expenditures of an average middle class American family.

The current population numbers of different cities in the United States

**Correct answer:**

The decrease in weight of a dieting adult male over the last 12 months

The line graph is best used with data that occurs sequentially, especially sequentially over a period of time. The line graph is best at describing a general trend, such as an increase or decrease, over time.

The decrease in weight of an adult male over 12 months fits a line graph well because there is data that can be organized sequentially (chronologically, in this case) and because we would be looking for some sort of trend in the data, a decrease over time in this case.

### Example Question #1 : Summarize And Interpret Data Presented Verbally, Tabularly, And Graphically

The approximate salaries of employees in a company are given by the histogram below:

Using the data presented in the histogram, determine what percentage of employees earn a weekly salary of $180,000 or more.

**Possible Answers:**

**Correct answer:**

Each bar in this histogram represent the percent of employees with salary in the given range. For example, the bar above the label "150–159" means that 25% of the employees earn between $150,000 and $159,000.

Since we want the percent of employees who earn $180,000 or more, we need to add the values for the bars for "180–189", "190–199", and "200–210".

The bars show that 15% of employees earn between $180,000 and $189,000, 15% earn between $190,000 and $199,000, and 5% earn between $200,000 and $210,000.

Adding these percentages together yields 35%.

### Example Question #1 : Data Analysis, Probability, And Statistics

The yearly revenue over 10 years of a company is given by the following graph.

Using the graph, determine the approximate revenue in the year 2004.

**Possible Answers:**

**Correct answer:**

The question asks for you to find the revenue in the year 2004. The horizontal axis is labeled "Year," so look there first to find where the label for 2004 is.

Tracing upwards, you will see that the value 2004 corresponds to a value of about 16 on the vertical axis. Since the label for the vertical axis is "Dollars in Millions," this means that the revenue in 2004 was 16 million dollars.

In numerical form, 16 million dollars is $16,000,000.

### Example Question #1 : Data Analysis, Probability, And Statistics

Determine the linear regression line for the following paired data:

**Possible Answers:**

**Correct answer:**

The formula for a regression line for a set of paired data is the line of the equation

,

where

and

.

, the number of pairs.

is the sum of the values:

is the sum of the values:

is the sum of the squares of the values:

is the sum of the products:

Substituting:

and are the arithmetic means of the and values, respectively - the sums divided by the number of values:

The equation of the linear regression line is .

### Example Question #1 : Data Analysis, Probability, And Statistics

Determine the linear regression line for the following paired data:

**Possible Answers:**

**Correct answer:**

The formula for a regression line for a set of paired data is the line of the equation

,

where

and

.

, the number of pairs.

is the sum of the values:

is the sum of the values:

is the sum of the squares of the values:

is the sum of the products:

Substituting:

and are the arithmetic means of the and values, respectively - the sums divided by the number of values:

The linear regression line is the line of the equation .

### Example Question #1 : Single Events

What is the probability that a person will roll an even number on a six-sided fair die?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

The die has six sides with the following values: one tow, three, four, five, and six. Of these values the die has three that are even: two, four, and six. We can write the following probability.

Simplify.

Now, let's convert this into a percentage:

### Example Question #1 : Single Events

Two fair dice are tossed. You are not shown the dice but you are told that exactly one die shows an even number. Give the probability that a total of seven was thrown.

**Possible Answers:**

**Correct answer:**

Two fair dice can be thrown with 36 equally probable rolls. 18 rolls comprise one even number and one odd number. They are as follows - with the rolls that total seven in **boldface**:

6 of the 18 possible rolls have total 7, making the probability of a roll of 7, given that exactly one doe shows an even number, equal to .

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