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# Step-by-Step Math Answer

Median is the middle value in a set of data arranged numerically.

So, first arrange the set of data in ascending order. We get:

set A: 1, 1, 2, 3, 3, 4, 5, 6, 7, 7, 8, 9, 9, 10, 12, 13So, the middle value is the average of the eighth and ninth values.

The eighth and the ninth values are 6 and 7 respectively.

Hence, the median of the set of data is 6.5.

The lower quartile is the median of the lower half of the data set.

The lower quartile is the median of the lower half of the data set.

Since, there are 16 values the first 8 values are the lower half.

So, the values in the lower half are:

1, 1, 2, 3, 3, 4, 5, 6

Here, there are two middle values, 3 and 3. So, the median is their average, 3.

Therefore, the lower quartile is 3.

The upper quartile is the median of the upper half of the data set.

The upper quartile is the median of the upper half of the data set.

Since, there are 16 values the last eight values are the upper half.

So, the values in the upper half are:

7, 7, 8, 9, 9, 10, 12, 13

Here, there are two middle values, 9 and 9. So, the median is their average 9.

Therefore, the upper quartile is 9.

Consider data set B. First, arrange the set of data in ascending order.

So, first arrange the set of data in ascending order. We get:

set B: 1, 3, 4, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10So, the middle value is the average of the eighth and ninth values.

The eighth and the ninth values are 7 and 8 respectively.

Hence, the median of the set of data is 7.5.

The lower quartile is the median of the lower half of the data set:

1, 3, 4, 6, 6, 7, 7, 7

Here, there are two middle values, 6 and 6. So, the median is their average, 6.

Therefore, the lower quartile is 6.

The upper quartile is the median of the upper half of the data set:

8, 8, 8, 9, 9, 9, 10, 10

Here, there are two middle values, 9 and 9. So, the median is their average, 9.

Therefore, the upper quartile is 9.

Draw a number line, considering both the sets of data.

Draw a number line that includes the minimum data value, 1, and the maximum data value, 13.

Mark the least and greatest values, the medians and the quartiles.

Mark the least and greatest values, the medians and the quartiles.

Here, for data set A, the least and greatest values are 1 and 13, the median is 6.5 and the quartiles are 3 and 9.

See the figure.

Here, for data set B, the least and greatest values are 1 and 10, the median is 7.5 and the quartiles are 6 and 9.

See the figure.

Now, draw the boxes.

Draw each box from the first to the third quartile.

Also, mark each median with a vertical segment.

See the figure.

Draw whiskers.

Whiskers are line segments joining the quartiles to the maximum and the minimum values.

Draw whiskers from each box to the least and greatest values.

See the figure.