I am having trouble anwering the following problem:
The test scores from Mrs. Gray's math class are shown below.
72, 73, 66, 71, 82, 85, 86, 89, 91, 92
Construct a box-and-whisker plot to display this data.
I don't know how to begin answering this problem and what steps must be done in order for me to get the correct answer.
Duplicate question. See my previous answer.
To construct a box-and-whisker plot, you need to follow a few steps:
Step 1: Order the data from least to greatest.
In this case, the ordered data set is:
66, 71, 72, 73, 82, 85, 86, 89, 91, 92
Step 2: Find the minimum and maximum values.
The minimum value is 66, and the maximum value is 92.
Step 3: Find the median (middle value) of the data set.
Since we have an even number of data points, we need to find the average of the two middle values. In this case, the two middle values are 82 and 85, so the median is (82 + 85) / 2 = 83.5.
Step 4: Find the lower quartile (Q1).
To find Q1, you need to calculate the median of the lower half of the data set. In this case, the lower half is 66, 71, 72, 73, and 82. Since there is an odd number of values, the median is the middle value, which is 72.
Step 5: Find the upper quartile (Q3).
To find Q3, you need to calculate the median of the upper half of the data set. In this case, the upper half is 85, 86, 89, 91, and 92. Again, since there is an odd number of values, the median is the middle value, which is 89.
Step 6: Calculate the interquartile range (IQR).
The IQR is the difference between Q3 and Q1. In this case, IQR = 89 - 72 = 17.
Step 7: Draw the box-and-whisker plot.
To construct the plot, draw a number line with the minimum value (66) on the left and the maximum value (92) on the right. Then, draw a box from Q1 (72) to Q3 (89), with the median (83.5) marked inside. Finally, draw "whiskers" extending from the box to the minimum value (66) and the maximum value (92).