How do you create a box plot for the data set {1, 12, 2, 9, 2, 3, 7, 3, 3, 6)?

Question

Christopher Axton · Accepted Answer

The raw data is:

# {1, 12, 2, 9, 2, 3, 7, 3, 3, 6} #

First we arrange in ascending order:

# {1, 2, 2, 3, 3, 3, 6, 7, 9, 12} #

We the calculate the media, #Q_2#, which is the middle value, and as we have an even number of data points will be an average:

# Q_2 = 1/2(3+3) = 3 #

Similarly we calculate the lower and upper quartiles:

# Q_1 = 2 #
# Q_3 = 7 #

So then we have enough information to draw the box and whisker diagram:

Emery Adams · Answer

undefined To create a box plot for the given data set {1, 12, 2, 9, 2, 3, 7, 3, 3, 6}, you would follow these steps:

1. Arrange the data set in ascending order: {1, 2, 2, 3, 3, 3, 6, 7, 9, 12}.
2. Calculate the five-number summary: minimum, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and maximum.
3. The minimum value is 1.
4. Q1 is the median of the lower half of the data, which is 2.
5. Q2 is the median of the entire data set, which is 3.
6. Q3 is the median of the upper half of the data, which is 7.
7. The maximum value is 12.
8. Plot a number line that spans from the minimum to the maximum value.
9. Draw a box from Q1 to Q3, with a line inside representing the median (Q2).
10. Add "whiskers" extending from the box to the minimum and maximum values.
11. Identify any outliers, which are data points that fall outside the range of Q1 - 1.5 * IQR to Q3 + 1.5 * IQR, where IQR is the interquartile range (Q3 - Q1).
12. Mark the outliers on the plot.

This completes the construction of the box plot for the given data set.