Summarize and interpret data presented verbally, tabularly, and graphically - HiSET

Card 0 of 32

Question

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

Answer

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

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$b_{1} = \frac{4 (62.1)-(10)( 22.0)}{4(30)-(10)^{2}}$

$= \frac{248.4-220}{120-100}$

$= \frac{28.4}{20}$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{22}{4} = 5.5$

$b_{0} = \overline{y} - b_{1}\overline{x}$

$b_{0} =5.5 - 1.42 (2.5)$

The equation of the linear regression line is .

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Question

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

Answer

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

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$b_{1} = \frac{4 (68.7)-(10)( 30.8)}{4(30)-(10)^{2}}$

$= \frac{274.8 - 308}{120-100 }$

$= \frac{-33.2}{20 }$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{30.8}{4} = 7.7$

$b_{0} = \overline{y} - b_{1}\overline{x}$

The linear regression line is the line of the equation .

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Question

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?

Answer

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%.

Compare your answer with the correct one above

Question

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.

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.

Compare your answer with the correct one above

Question

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.

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%.

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Question

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

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

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

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

Answer

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.

Compare your answer with the correct one above

Question

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

Answer

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

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$b_{1} = \frac{4 (62.1)-(10)( 22.0)}{4(30)-(10)^{2}}$

$= \frac{248.4-220}{120-100}$

$= \frac{28.4}{20}$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{22}{4} = 5.5$

$b_{0} = \overline{y} - b_{1}\overline{x}$

$b_{0} =5.5 - 1.42 (2.5)$

The equation of the linear regression line is .

Compare your answer with the correct one above

Question

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

Answer

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

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$b_{1} = \frac{4 (68.7)-(10)( 30.8)}{4(30)-(10)^{2}}$

$= \frac{274.8 - 308}{120-100 }$

$= \frac{-33.2}{20 }$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{30.8}{4} = 7.7$

$b_{0} = \overline{y} - b_{1}\overline{x}$

The linear regression line is the line of the equation .

Compare your answer with the correct one above

Question

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?

Answer

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%.

Compare your answer with the correct one above

Question

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.

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.

Compare your answer with the correct one above

Question

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.

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%.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

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

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

Answer

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.

Compare your answer with the correct one above

Question

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

Answer

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

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$b_{1} = \frac{4 (62.1)-(10)( 22.0)}{4(30)-(10)^{2}}$

$= \frac{248.4-220}{120-100}$

$= \frac{28.4}{20}$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{22}{4} = 5.5$

$b_{0} = \overline{y} - b_{1}\overline{x}$

$b_{0} =5.5 - 1.42 (2.5)$

The equation of the linear regression line is .

Compare your answer with the correct one above

Question

Determine the linear regression line for the following paired data:

$\begin{matrix} \underline{x }&\underline{y} \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

Answer

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

$y =b_{1}x+ b_{0}$ ,

where

$b_{1} = \frac{n (\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}$

and

$b_{0} = \overline{y} - b_{1}\overline{x}$ .

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum x^{2}$ is the sum of the squares of the values:

$\sum x^{2} = 1^{2} + 2^{2} + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$b_{1} = \frac{4 (68.7)-(10)( 30.8)}{4(30)-(10)^{2}}$

$= \frac{274.8 - 308}{120-100 }$

$= \frac{-33.2}{20 }$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$\overline{x} = \frac{\sum x}{n} = \frac{10}{4} = 2.5$

$\overline{y} = \frac{\sum y}{n} = \frac{30.8}{4} = 7.7$

$b_{0} = \overline{y} - b_{1}\overline{x}$

The linear regression line is the line of the equation .

Compare your answer with the correct one above

Question

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?

Answer

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%.

Compare your answer with the correct one above

Question

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.

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.

Compare your answer with the correct one above

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