After giving a statistics exam, Professor Dang determined the following five-number summary for her class results.
60
67
77
90
98
Use this information to draw a boxplot of the exam scores.
To draw a boxplot of the exam scores using the given five-number summary, follow these steps:
Step 1: Define the scale of the number line. In this case, we will use a scale of 10 (from 0 to 100) based on the maximum and minimum values of the data.
Step 2: Place a number line horizontally and label it from 0 to 100, with a tick mark for each multiple of 10.
Step 3: Plot the minimum value (60) as a small tick mark on the number line, representing the left-most edge of the boxplot.
Step 4: Plot the first quartile (Q1) value (67) as a short horizontal line to the right of the minimum value mark.
Step 5: Plot the median (also known as the second quartile, Q2) value (77) as a longer line above the first quartile mark.
Step 6: Plot the third quartile (Q3) value (90) as a short horizontal line to the right of the median mark.
Step 7: Plot the maximum value (98) as a small tick mark to the right of the third quartile mark.
Step 8: Connect the first quartile mark, median mark, and third quartile mark with vertical lines to form the box of the boxplot.
Step 9: Draw a vertical line from the minimum value mark to the bottom of the box, and another vertical line from the maximum value mark to the top of the box to represent the "whiskers."
Step 10: Optionally, label the key values (minimum, first quartile, median, third quartile, and maximum).
The completed boxplot should look like this:
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| |..........................
60 77 98
To draw a boxplot using the given five-number summary, follow these steps:
Step 1: Determine the minimum and maximum values:
The minimum value is 60, and the maximum value is 98.
Step 2: Locate the median:
The median is the middle value, which is 77.
Step 3: Find the lower quartile:
The lower quartile (Q1) is the median of the lower half of the data. In this case, it is 67.
Step 4: Find the upper quartile:
The upper quartile (Q3) is the median of the upper half of the data. In this case, it is 90.
Step 5: Calculate the Interquartile Range (IQR):
The IQR is the difference between Q3 and Q1. In this case, IQR = Q3 - Q1 = 90 - 67 = 23.
Step 6: Determine any outliers:
Any values below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR are considered outliers. However, since all the given values fall within the minimum and maximum values, there are no outliers in this case.
Step 7: Draw the boxplot:
On a number line or x-axis, mark the minimum value (60) on the left side and the maximum value (98) on the right side. Draw a vertical line connecting them.
Next, draw a box starting from Q1 (67) and ending at Q3 (90). Draw a line through the box at the position of the median (77).
The resulting boxplot represents the exam scores as follows:
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60 67 77 90 98
Note: The boxplot may appear differently depending on the software or tool used to create it, but the general structure remains the same.