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

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 = 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:

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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:

- Arrange the data set in ascending order: {1, 2, 2, 3, 3, 3, 6, 7, 9, 12}.
- Calculate the five-number summary: minimum, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and maximum.
- The minimum value is 1.
- Q1 is the median of the lower half of the data, which is 2.
- Q2 is the median of the entire data set, which is 3.
- Q3 is the median of the upper half of the data, which is 7.
- The maximum value is 12.
- Plot a number line that spans from the minimum to the maximum value.
- Draw a box from Q1 to Q3, with a line inside representing the median (Q2).
- Add "whiskers" extending from the box to the minimum and maximum values.
- 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).
- Mark the outliers on the plot.

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

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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