Algebra II : Algebra II

Example Questions

Example Question #1 : Box And Whisker Plots

Draw a Box and Whisker plot for the following data set.

Explanation:

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.

Example Question #2 : Box And Whisker Plots

Draw a Box and Whisker plot for the following data set.

Explanation:

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:

Example Question #2 : Box And Whisker Plots

Draw a box and whisker plot for the following data set.

Explanation:

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:

Example Question #3 : Box And Whisker Plots

Draw a Box and Whisker plot for the following data set.

Explanation:

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.

Example Question #4 : Box And Whisker Plots

Draw a Box and Whisker plot for the following data set.

Explanation:

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:

Example Question #5 : Box And Whisker Plots

Draw a Box and Whisker plot for the following data set.

Explanation:

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:

Example Question #6 : Box And Whisker Plots

The box and whisker plot above can be used to find all of the following information about the data set that it describes except:

Range

Median Value

Maximum and minimum values

The 4 quartiles of the data set

The box and whisker plot gives you all of these.

The box and whisker plot gives you all of these.

Explanation:

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"

Example Question #1 : Histograms

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?

Explanation:

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.

Example Question #2 : Histograms

Refer to the above bar graph.

How many students at Polk Middle School scored above 550 on the math portion of the SCAT?

The answer to the question cannot be derived from the graph.

The answer to the question cannot be derived from the graph.

Explanation:

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.

Example Question #1 : Histograms

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?