Representing Data - Algebra II
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Draw a Box and Whisker plot for the following data set.
Draw a Box and Whisker plot for the following data set.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile: 
, 
, 
Median of 1st quartile: 
2nd quartile = Median of total set: 
3rd quartile: 
, 
, 
Median of 3rd quartile: 
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
The endpoints (black dots) represent the smallest and largest values, in this case, 2 and 39.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile:
Median of 1st quartile:
2nd quartile = Median of total set:
3rd quartile:
Median of 3rd quartile:
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
The endpoints (black dots) represent the smallest and largest values, in this case, 2 and 39.
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Draw a Box and Whisker plot for the following data set.
Draw a Box and Whisker plot for the following data set.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile: 
Median of 1st quartile: 
2nd quartile = Median: 
3rd quartile:
Median of 3rd quartile: 
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile:
Median of 1st quartile:
2nd quartile = Median:
3rd quartile:
Median of 3rd quartile:
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
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Draw a box and whisker plot for the following data set.
Draw a box and whisker plot for the following data set.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile: 
Median of 1st quartile: 
2nd quartile = Median: 
3rd quartile: 
Median of 3rd quartile: 
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile:
Median of 1st quartile:
2nd quartile = Median:
3rd quartile:
Median of 3rd quartile:
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
Compare your answer with the correct one above
Draw a Box and Whisker plot for the following data set.
Draw a Box and Whisker plot for the following data set.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile: 
Median of 1st quartile: 
2nd quartile= Median: 
3rd quartile: 
Median of 3rd quartile: 
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile:
Median of 1st quartile:
2nd quartile= Median:
3rd quartile:
Median of 3rd quartile:
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines.
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Draw a Box and Whisker plot for the following data set.
Draw a Box and Whisker plot for the following data set.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile: 
Median of 1st quartile: 
2nd quartile = Median: 
3rd quartile: 
Median of 3rd quartile: 
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile:
Median of 1st quartile:
2nd quartile = Median:
3rd quartile:
Median of 3rd quartile:
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
Compare your answer with the correct one above
Draw a Box and Whisker plot for the following data set.
Draw a Box and Whisker plot for the following data set.
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile: 
Median of 1st quartile: 
2nd quartile = Median: 
3rd quartile: 
Median of 3rd quartile: 
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
Put the data in numerical order (from smallest to largest) if it isn't already. In order to find the median, divide the data into two halves. In order to divide the values into quartiles, find the median of the two halves.
1st quartile:
Median of 1st quartile:
2nd quartile = Median:
3rd quartile:
Median of 3rd quartile:
To construct the Box and Whisker Plot we use the minimum and the maximum value in the data set as the ends of the whiskers. To construct the box, we plot a line at the median of the 1st quartile, the median of our total data set, and at the median of the 3rd quartile. Then we connect the tops and bottom of the lines. The result is as follows:
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The box and whisker plot above can be used to find all of the following information about the data set that it describes except:
The box and whisker plot above can be used to find all of the following information about the data set that it describes except:
The median value of the data set, 86, is represented by the dashed line inside the box.
The maximum and minimum of the data set, 100 and 75 (respectively), are found at the far ends of the 2 whiskers on either end.
The range of the data set is found by subtracting the minimum from the maximum; 100-75=25, so the range is 25.
The upper and lower quartiles are given by the two boundaries between the box and the whiskers: the lower quartile (1st quartile) is the left boundary, 80 in the data set; the upper quartile (3rd quartile) is the right boundary, which is 92 in the data set.
All of the other choices are provided by the box and whisker plot, so the correct choice is "The box and whisker plot gives you all of these"
The median value of the data set, 86, is represented by the dashed line inside the box.
The maximum and minimum of the data set, 100 and 75 (respectively), are found at the far ends of the 2 whiskers on either end.
The range of the data set is found by subtracting the minimum from the maximum; 100-75=25, so the range is 25.
The upper and lower quartiles are given by the two boundaries between the box and the whiskers: the lower quartile (1st quartile) is the left boundary, 80 in the data set; the upper quartile (3rd quartile) is the right boundary, which is 92 in the data set.
All of the other choices are provided by the box and whisker plot, so the correct choice is "The box and whisker plot gives you all of these"
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Refer to the above graph. Carla, a sixth grader at Polk, outscored 101 of the students who took the test. Which of these could her score have been?
Refer to the above graph. Carla, a sixth grader at Polk, outscored 101 of the students who took the test. Which of these could her score have been?
students achieved scores between 200 and 600, and Carla outscored all of them.
students achieved scores between 200 and 700. However, Carla did not outscore all of them.
Carla's score had to have been between 600 and 700, so of the five choices, 660 is the only possible one.
Carla's score had to have been between 600 and 700, so of the five choices, 660 is the only possible one.
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Above is a stem-and-leaf representation of the scores on a test administered to a group of students. What was the midrange of the scores?
Above is a stem-and-leaf representation of the scores on a test administered to a group of students. What was the midrange of the scores?
The midrange is the mean of the highest and lowest scores.
Each "stem" in the left column represents the tens digits of the scores; each of the numbers in its row, or "leaf" represents the units digits. The lowest score is represented by the 4 "leaf" in the "3" row - that is, it is 34 - and the highest score is represented by the 8 "leaf" in the "9" row - that is, 98. The midrange is therefore
The midrange is the mean of the highest and lowest scores.
Each "stem" in the left column represents the tens digits of the scores; each of the numbers in its row, or "leaf" represents the units digits. The lowest score is represented by the 4 "leaf" in the "3" row - that is, it is 34 - and the highest score is represented by the 8 "leaf" in the "9" row - that is, 98. The midrange is therefore
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Refer to the above bar graph.
How many students at Polk Middle School scored above 550 on the math portion of the SCAT?
Refer to the above bar graph.
How many students at Polk Middle School scored above 550 on the math portion of the SCAT?
The dividing points of the intervals used to classify students on this graph occur at multiples of 100. No details are given for each interval beyond the number of students who scored in it, so, for example, within the interval 500-600, it is not made clear how many of the 40 students scored above or below 550. The answer is that insufficient information is provided.
The dividing points of the intervals used to classify students on this graph occur at multiples of 100. No details are given for each interval beyond the number of students who scored in it, so, for example, within the interval 500-600, it is not made clear how many of the 40 students scored above or below 550. The answer is that insufficient information is provided.
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The following histogram shows the highest level of education attained by the employees of a local store.
How many employees are working for the store?
The following histogram shows the highest level of education attained by the employees of a local store.
How many employees are working for the store?
Solution
The height of each bar shows the number of employees who attained that particular level of education. So to find the total number of employees, we add the numbers shown by all the bars in the histogram.
The total number of employees is 200.
Solution
The height of each bar shows the number of employees who attained that particular level of education. So to find the total number of employees, we add the numbers shown by all the bars in the histogram.
The total number of employees is 200.
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The following histogram shows the highest level of education attained by the employees of a local store.
How many employees have at least an Associate degree?
The following histogram shows the highest level of education attained by the employees of a local store.
How many employees have at least an Associate degree?
Solution
The number of employees who have at least an Associate degree include the employees who have an Associate degree, the employees who have a Bachelor degree and the employees who have a Graduate degree.
We read the numbers from the 3 bars on the histogram showing the employees with Associate, Bachelor, and Graduate degrees.
Solution
The number of employees who have at least an Associate degree include the employees who have an Associate degree, the employees who have a Bachelor degree and the employees who have a Graduate degree.
We read the numbers from the 3 bars on the histogram showing the employees with Associate, Bachelor, and Graduate degrees.
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This histogram shows the distribution of grades on Mr. Margarine's final. What percentage of the students got an A or B?
This histogram shows the distribution of grades on Mr. Margarine's final. What percentage of the students got an A or B?
The histogram shows that there are a total of 23 students.
There were 7 students who earned B's and 5 who earned A's, so that's 12 who got A's or B's.
, or 
.
The histogram shows that there are a total of 23 students.
There were 7 students who earned B's and 5 who earned A's, so that's 12 who got A's or B's.
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Which of the following represents a positive association in a scatterplot?
Which of the following represents a positive association in a scatterplot?
A positive association is defined as a scatterplot on which the best fit line has a positive slope.
This pattern is identified because on the graph, looking from left to right, the vast majority of the points goes up.
This can also be described by saying, "as 
increases, 
increases".
A positive association is defined as a scatterplot on which the best fit line has a positive slope.
This pattern is identified because on the graph, looking from left to right, the vast majority of the points goes up.
This can also be described by saying, "as
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A scatterplot correlates adult males' height vs. shoe size. What does the point 
on the scatterplot represent?
A scatterplot correlates adult males' height vs. shoe size. What does the point
When creating a scatterplot, data is collected. This data is formulated into ordered pairs. Each of these ordered pairs, which are later graphed, represent one person's data. Thus, this particular piece of data would represent one man's height of 
inches and that same man's shoe size of 
.
When creating a scatterplot, data is collected. This data is formulated into ordered pairs. Each of these ordered pairs, which are later graphed, represent one person's data. Thus, this particular piece of data would represent one man's height of
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Which of the following would most likely represent an outlier on a scatterplot which relates height (in inches) to shoe size for men?
Which of the following would most likely represent an outlier on a scatterplot which relates height (in inches) to shoe size for men?
An outlier is defined as a point that does not fit within the general pattern of the data. Thus, we are looking for a height that is not within the normal range for an adult male, and shoe size which is outside of the range for an adult male. Typically, an adult male would be between 65 and 77 inches tall (5 feet 5 inches and 6 feet 5 inches). Typically, an adult male's shoe size would be around a 10. Thus, the outlier would have height and shoe size drastically different from these, 
.
An outlier is defined as a point that does not fit within the general pattern of the data. Thus, we are looking for a height that is not within the normal range for an adult male, and shoe size which is outside of the range for an adult male. Typically, an adult male would be between 65 and 77 inches tall (5 feet 5 inches and 6 feet 5 inches). Typically, an adult male's shoe size would be around a 10. Thus, the outlier would have height and shoe size drastically different from these,
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What type of correlation does this data have?
What type of correlation does this data have?
It has a positive correlation because the points all trend upward. In other words, as the independent variable on the x-axis increases, the dependent variable on the y-axis also increases. Therefore, the line of best fit that is drawn through the data represents a positive line as it has a positive slope. This verifies that our data has a positive correlation.
It has a positive correlation because the points all trend upward. In other words, as the independent variable on the x-axis increases, the dependent variable on the y-axis also increases. Therefore, the line of best fit that is drawn through the data represents a positive line as it has a positive slope. This verifies that our data has a positive correlation.
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This scatter plot represents data about snack quality (
-axis) vs. price (
-axis). Which statements are a correct interpretation of the data?
I. The price of a higher quality snack tends to be higher.
II. Points below the line represent snacks whose price is higher than their quality.
III. Points above the line represent snacks whose quality is higher than their price.
This scatter plot represents data about snack quality (
I. The price of a higher quality snack tends to be higher.
II. Points below the line represent snacks whose price is higher than their quality.
III. Points above the line represent snacks whose quality is higher than their price.
I. is a true statement about the scatter plot: as quality increases, price tends to increase.
II. is not true - the points under the line have a relatively low price compared to their quality.
III. is also not true - the points above the line have relatively low quality compared to their price.
I. is a true statement about the scatter plot: as quality increases, price tends to increase.
II. is not true - the points under the line have a relatively low price compared to their quality.
III. is also not true - the points above the line have relatively low quality compared to their price.
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What would be the most accurate line of best fit for this scatter plot?
What would be the most accurate line of best fit for this scatter plot?
This data is quadratic rather than linear - it increases much more sharply than the line 
. It is also a positive correlation, so the equation should be positive. It is not 
because the data starts very near the origin 
.
This data is quadratic rather than linear - it increases much more sharply than the line
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Above is a stem-and-leaf representation of the scores on a test administered to a group of students. What was the mode of the scores?
Above is a stem-and-leaf representation of the scores on a test administered to a group of students. What was the mode of the scores?
The mode of the data set is the score that occurs the most frequently.
Each "stem" in the left column represents the tens digits of the scores; each of the numbers in its row, or "leaf" represents the units digits. The entry that occurs the most frequently is represented by the "6" in the "7" row, so 76 is the one and only mode.
The mode of the data set is the score that occurs the most frequently.
Each "stem" in the left column represents the tens digits of the scores; each of the numbers in its row, or "leaf" represents the units digits. The entry that occurs the most frequently is represented by the "6" in the "7" row, so 76 is the one and only mode.
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